Exhibit 10.1

SPONSOR GUARANTEE

May 1, 2014

This Sponsor Guarantee (this “Guarantee”) is made and entered into as of the date set forth above by Mill Road Capital II, L.P., a Delaware limited partnership (the “Guarantor”), in favor and for the benefit of R. G. Barry Corporation, an Ohio corporation (the “Company”). Capitalized terms used in this Guarantee but not otherwise defined herein have the respective meanings given to such terms in that certain Agreement and Plan of Merger, dated as of the date hereof (as amended, amended and restated, supplemented or otherwise modified from time to time, the “Merger Agreement”), by and among Company, MRGB Hold Co., a Delaware corporation (“Parent”), and MRVK Merger Co., an Ohio corporation (“Merger Sub”).

1. Guarantee; Obligations. To induce the Company to enter into the Merger Agreement, pursuant to which, and subject to the terms and conditions thereof, Merger Sub will merge with and into the Company, with the Company as the Surviving Corporation, the Guarantor absolutely, unconditionally, and irrevocably guarantees to the Company, pursuant to the terms and subject to the conditions herein, the due, punctual and complete payment and performance of the payment obligations of Parent to pay, as applicable (i) contingent upon the Closing, and when and if due after the Effective Time, the Equity Portion of the Payment Fund, (ii) when and if due, any amounts that Parent has agreed to reimburse the Company pursuant to Section 6.5(b) of the Merger Agreement, and (iii) when and if due, the Parent Termination Fee (such amounts, as applicable, the Guarantor’s “Obligations”). All payments by Guarantor hereunder shall be made in immediately available United States funds. Solely with respect to the Guarantor’s Obligations under Sections 1(ii) and (iii), but not with respect to the Guarantor’s Obligations under Section 1(i) to pay the Equity Portion of the Payment Fund, Guarantor reserves the right to (a) set-off any amount owed under such Obligations by the Guarantor against any payment owing by the Company to Parent, Merger Sub, the Guarantor or any of their respective affiliates, and (b) assert any and all defenses which Parent or Merger Sub may have to payment of such Obligations. The parties hereto agree that this Guarantee may not be enforced without giving effect to limitations on the Guarantor’s liability in the amount of its Obligations. For the purposes hereof, “Equity Portion” means the total amount resulting from (w) the aggregate amount of the Payment Fund, plus, (x) the aggregate amount of the payment obligations of the Surviving Corporation under Section 2.3 of the Merger Agreement, minus (y) the aggregate amount of the Debt Financing (or any Alternative Financing) contemplated by the Debt Commitment Letter, and minus (z) the Company’s cash and short term marketable securities as of the Effective Time.

2. Unconditional Guarantee. The Company shall not be obligated to file any claim relating to the Obligations in the event that Parent or Merger Sub becomes subject to a bankruptcy, reorganization or similar proceeding, and the failure of the Company to so file shall not affect the Guarantor’s obligations hereunder. This is an unconditional guarantee of payment and performance and not of collectibility, and one or more separate actions may be brought and prosecuted against Guarantor to enforce this Guarantee, irrespective of whether any action is brought against Parent or Merger Sub or whether Parent or Merger Sub is joined in any such action or actions, provided that Guarantor shall have the right to assert defenses that Parent or Merger Sub may have to the payment of any Obligations under the terms of the Merger Agreement, other than any such defense arising out of, due to, or as a result of, the insolvency or bankruptcy of Parent or Merger Sub. If any payment by Parent or Merger Sub of the Obligations

is rescinded or must otherwise be returned for any reason whatsoever (other than pursuant to the terms of the Merger Agreement or due to a breach of the Merger Agreement by the Company), the Guarantor shall remain liable hereunder with respect to the Obligations (plus any Prevailing Party Cost, as defined in Section 16 below) as if such payment had not been made.

3. Changes in Obligations; Certain Waivers.

(a) The Guarantor agrees that the Company may, at any time and from time to time, without notice to or further consent of the Guarantor, make any agreement with Parent or Merger Sub for the extension, renewal, payment, compromise, discharge, or release of any of the Obligations, in whole or in part, or for any modification of the terms thereof or of any agreement between the Company and Parent or Merger Sub without in any way impairing or affecting this Guarantee. The Guarantor agrees that the obligations of the Guarantor hereunder shall not be released or discharged, in whole or in part, or otherwise affected by (i) the failure of the Company to assert any claim or demand or to enforce any right or remedy against Parent or Merger Sub with respect to the Obligations; (ii) any agreement with Parent or Merger Sub with respect to (a) any change in the time, place or manner of payment of any of the Obligations, (b) any rescission, waiver, compromise, consolidation, or other amendment or modification of any of the terms or provisions of the Merger Agreement or (c) any other agreement evidencing, securing, or otherwise executed in connection with any of the Obligations; (iii) any change in the corporate existence, structure or ownership of Parent or Merger Sub; (v) any insolvency, bankruptcy, reorganization, or other similar proceeding affecting Parent or Merger Sub; (vi) the existence of any claim, set-off or other right that the Guarantor may have at any time against Parent or Merger Sub, whether in connection with the Merger Agreement, the Obligations, or otherwise; or (vi) the adequacy of any other means the Company may have of obtaining payment of any of the Obligations.

(b) To the fullest extent permitted by law, the Guarantor hereby expressly waives any and all rights or defenses arising by reason of any law that would otherwise require any election of remedies by the Company. The Guarantor waives promptness, diligence, notice of the acceptance of this Guarantee and of the Obligations, presentment, demand for payment, notice of non-performance, default, dishonor and protest, notice of any Obligations incurred and any and all other notices of any kind (except for notices required to be provided to Parent and Merger Sub under the Merger Agreement), all defenses that may be available by virtue of any valuation, stay, moratorium law, or other similar law now or hereafter in effect, any right to require the marshalling of assets of Parent or Merger Sub with respect to any of the Obligations, and all suretyship defenses generally (whether at law or in equity), other than breach by the Company of this Guarantee. The Guarantor acknowledges that, as an Affiliate of Parent and Merger Sub, it will receive substantial direct and indirect benefits from the transactions contemplated by the Merger Agreement and that the waivers set forth in this Guarantee are knowingly made in contemplation of such benefits and after the advice of counsel.

4. No Waiver; Cumulative Rights. No failure on the part of the Company to exercise, and no delay in exercising, any right, remedy or power hereunder shall operate as a waiver thereof, nor shall any single or partial exercise by the Company of any right, remedy or power hereunder preclude any other or future exercise of any right, remedy or power. Each and

2

every right, remedy and power hereby granted to the Company or allowed it by law or other agreement shall be cumulative and not exclusive of any other, and may be exercised by the Company at any time or from time to time. The Company shall not have any obligation to proceed at any time or in any manner against, or exhaust any or all of the Company’s rights against, Parent or Merger Sub prior to proceeding against Guarantor. Following the Effective Time, the rights of the Company under this Guarantee may not be waived without the written consent of a majority of the individuals who were serving as directors of the Company immediately prior to the Effective Time.

5. Representations and Warranties. The Guarantor hereby represents and warrants to the Company that:

(a) the Guarantor has full power and authority to execute and deliver this Guarantee and to pay and perform the Obligations;

(b) the execution, delivery and performance of this Guarantee have been duly authorized by all necessary corporate, partnership or limited liability company action and do not contravene any provision of the Guarantor’s charter, partnership agreement, operating agreement, or similar organizational documents or any law, regulation, rule, decree, order, judgment, or contractual restriction binding on the Guarantor or its assets;

(c) all consents, approvals, authorizations, permits of, or filings with and notifications to, any governmental authority necessary for the due execution, delivery and performance of this Guarantee by the Guarantor have been obtained or made, and all conditions thereof have been duly complied with, and no other action by, and no notice to or filing with, any governmental authority or regulatory body is required in connection with the execution, delivery or performance of this Guarantee;

(d) this Guarantee constitutes a legal, valid and binding obligation of the Guarantor, enforceable against the Guarantor in accordance with its terms, subject to (i) the effects of bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium or other similar laws affecting creditors’ rights generally, and (ii) general equitable principles (whether considered in a proceeding in equity or at law); and

(e) Guarantor has the financial capacity to pay and perform its obligations under this Guarantee, and all funds necessary for the Guarantor to fulfill its Obligations under this Guarantee are currently available to Guarantor and shall remain available to the Guarantor for so long as this Guarantee shall remain in effect in accordance with Section 8 hereof.

6. Assignment. The Guarantor may not assign or delegate, as applicable, its rights, interests, or obligations hereunder to any other person (whether by operation of law or otherwise) without the prior written consent of the Company. The rights of the Company under this Guarantee may not be assigned without the prior written consent of Guarantor; provided, however, that, following the Effective Time, the rights of the Company under this Guarantee may not be assigned without the written consent of a majority of the individuals who were serving as directors of the Company immediately prior to the Effective Time.

3

7. Notices. All notices, requests and other communications given or made pursuant to this Guarantee shall be in writing (including facsimile transmission) and shall be given as follows:

Mill Road Capital II, L. P.

382 Greenwich Avenue, Suite 1

Greenwich, Connecticut 06830

Facsimile No.: (203) 621-3280

Attention: Scott Scharfman

with a copy (not constituting notice) to:

Foley Hoag LLP

Seaport West

155 Seaport Boulevard

Boston, Massachusetts 02210

Facsimile No.: (617) 832-7000

Attention: Peter M. Rosenblum, Esq. and Mark A. Haddad, Esq.

R.G. Barry Corporation

13405 Yarmouth Road N.W.

Pickerington, Ohio 43147

Facsimile No.: (614) 729-7293

Attention: Jose G. Ibarra, Senior Vice President and CFO

with a copy (not constituting notice) to:

Vorys, Sater, Seymour and Pease LLP

301 E. Fourth Street, Suite 3500

Cincinnati, Ohio 45202

Facsimile No.: (513) 852-8490

Attention: Roger E. Lautzenhiser, Esq. and Michael A. Cline, Esq.

or to such other address or facsimile number as the party entitled to receive such notice may hereafter specify for the purpose. All such notices, requests and other communications shall be deemed received (a) on the date of delivery if delivered personally, (b) on the date of confirmation of receipt of transmission by facsimile transmission, or (c) on the date of confirmation of receipt if delivered by an internationally recognized courier service.

8. Termination. This Guarantee shall terminate as of the earlier of (a) the termination of the Merger Agreement, in accordance with its terms, and if applicable in such case, the payment in full of the Obligations under Sections

4

1(ii) and (iii) by any combination of Parent, Merger Sub and/or the Guarantor or (b) upon the closing of the Merger, and the payment in full of the Obligations under Section 1(i) by Parent (from the Equity Financing contributed by Guarantor) or by Guarantor directly (the “Termination Time”). This Guarantee shall remain in full force and effect and shall be binding on the Guarantor and its successors and assigns with respect to each Obligation until such Termination Time, and none of Guarantor, Parent, Merger Sub or the Surviving Corporation shall have any obligations hereunder following the Termination Time.

9. Governing Law. This Guarantee shall be governed by, construed, and enforced in accordance with the laws of the State of Ohio applicable to contracts executed in and to be performed in that State, without giving effect to the conflict or choice of law provisions thereof that would give rise to the application of the domestic substantive law of any other jurisdiction. All actions arising out of or relating to this Guarantee shall be heard and determined exclusively in the state and federal courts located in the State of Ohio, County of Franklin. Each of the Guarantor and the Company hereby (a) irrevocably submits to the exclusive jurisdiction of any of these courts sitting in the State of Ohio (and of the appellate courts therefrom) for the purpose of any action arising out of or relating to this Guarantee, and (b) irrevocably waives, and agrees not to assert by way of motion, defense, or otherwise in any such action, any claim that it is not subject personally to the jurisdiction of the above-named courts, that its property is exempt or immune from attachment or execution, that the action is brought in an inconvenient forum, that the venue of the action is improper, or that this Guarantee or the transactions contemplated hereby may not be enforced in or by the above-named courts.

10. Waiver of Jury Trial. EACH OF THE GUARANTOR AND THE COMPANY HEREBY EXPRESSLY WAIVES, TO THE FULLEST EXTENT PERMITTED BY APPLICABLE LAW, ANY RIGHT TO TRIAL BY JURY OF ANY CLAIM, DEMAND, ACTION, OR CAUSE OF ACTION (A) ARISING UNDER THIS GUARANTEE OR THE TRANSACTIONS CONTEMPLATED HEREBY, OR (B) IN ANY WAY CONNECTED WITH OR RELATED OR INCIDENTAL TO THIS GUARANTEE OR THE TRANSACTIONS CONTEMPLATED HEREBY, IN EACH CASE WHETHER NOW EXISTING OR HEREAFTER ARISING, AND WHETHER SOUNDING IN CONTRACT OR TORT OR OTHERWISE; AND EACH OF THE GUARANTOR AND THE COMPANY HEREBY AGREES AND CONSENTS THAT ANY SUCH CLAIM, DEMAND, ACTION, OR CAUSE OF ACTION SHALL BE DECIDED BY COURT TRIAL WITHOUT A JURY, AND THAT THE OTHER PARTY MAY FILE AN ORIGINAL COUNTERPART OR A COPY OF THIS SECTION WITH ANY COURT AS WRITTEN EVIDENCE OF THE CONSENT OF SUCH PARTY TO THE WAIVER OF SUCH PARTY’S RIGHT TO TRIAL BY JURY.

11. Counterparts. This Guarantee may be executed in two or more counterparts, each of which will be deemed an original but all of which will constitute one instrument, and by facsimile or electronic transmission (including by .pdf).

12. Entire Agreement. This Guarantee and the Merger Agreement constitute the entire agreement with respect to the subject matter hereof and supersede any and all prior discussions, negotiations, proposals, undertakings, understandings and agreements, whether written or oral, among Parent, Merger Sub and the Guarantor or any of their respective affiliates, on the one hand, and the Company or any of its affiliates on the other hand, with respect to such subject matter only.

5

13. Amendment. This Guarantee may not be amended except by an instrument in writing signed by the parties hereto; provided, however, that, following the Effective Time, this Guarantee may not be amended without the written consent of a majority of the individuals who were serving as directors of the Company immediately prior to the Effective Time.

14. Severability. If any term or other provision of this Guarantee is invalid, illegal or incapable of being enforced by rule of law, or public policy, all other conditions and provisions of this Guarantee shall nevertheless remain in full force and effect.

15. No Subrogation. The Guarantor hereby unconditionally and irrevocably waives and agrees not to exercise any rights that it may now have or hereafter acquire against one or both of Parent and Merger Sub that arise from the existence, payment, performance, or enforcement of the Guarantor’s obligations under or in respect of this Guarantee or any other agreement in connection therewith, including, without limitation, any right of subrogation, reimbursement, exoneration, contribution or indemnification and any right to participate in any claim or remedy of the Company against one or both of Parent or Merger Sub, whether or not such claim, remedy or right arises in equity or under contract or any applicable law, including, without limitation, the right to take or receive from one or both of Parent or Merger Sub, directly or indirectly, in cash or other property or by set-off or in any other manner, payment or security on account of such claim, remedy or right, unless and until all of the Obligations and Prevailing Party Costs (as defined below), if applicable, shall have been terminated or paid in full or, in the case of the Obligations, fully provided for by the irrevocable deposit of immediately available funds to the Payment Fund described in Section 2.2 of the Merger Agreement. If any amount shall be paid to the Guarantor in violation of the immediately preceding sentence at any time prior to the payment in full in cash of the Obligations and Prevailing Party Costs, if applicable, such amount shall be received and held in trust for the benefit of the Company, shall be segregated from other property and funds of the Guarantor and shall forthwith be paid or delivered to the Company in the same form as so received (with any necessary endorsement or assignment) to be credited and applied to the Obligations and Prevailing Party Costs, if applicable, whether matured or unmatured.

16. Costs and Expenses. In any action at law or suit in equity to enforce this Guarantee or the rights of any of the parties hereunder, the prevailing party in such action or suit shall be entitled to recover from the non-prevailing party its reasonable and documented attorneys’ fees and all other reasonable court costs and expenses incurred in such action or suit (“Prevailing Party Costs”). The parties agree that the determination of who is the prevailing party and the amount of such costs and expenses shall be made by the court in any such action.

[Remainder of page intentionally blank; signatures follow]

6

IN WITNESS WHEREOF, this Guarantee has been duly executed and delivered by the Guarantor to the Company as of the date first above written.

[Signature Page to Sponsor Guarantee]

7