Exhibit 4.1

GMS Ventures & Investments

Intertrust Corporate Services(Cayman)Ltd, 190 Elgin Avenue, George Town

Grand Cayman, E9, KYI-9007

962 6 582 7999

May 28, 2026

Re: Amendment to Existing Warrants

Ladies and Gentlemen:

Reference is hereby made to the registered direct offering on or about the date hereof (the “Offering”) by Outlook Therapeutics, Inc. (the “Company”) of shares of the Company’s common stock (collectively, the “Shares”). Capitalized terms used but not otherwise defined herein shall have the set forth in the Existing Warrants (as defined below).

This letter confirms that, in consideration for the Holder’s participation in the Offering and purchase of Shares in the Offering (the “Purchase Commitment”), the Company hereby amends, effective as of the closing of the Offering, the Holder’s existing (i) Tranche A warrants to purchase up to 3,458,571 shares of common stock of the Company and Tranche B warrants to purchase up to 3,458,571 shares of common stock of the Company, each issued on January 16, 2025, at an exercise price of $2.26 per share, and (ii) warrants to purchase up to 8,571,428 shares of common stock of the Company, issued on May 27, 2025, at an exercise price of $1.40 per share, in each case between the Company and the Holder named therein ((i) and (ii) collectively, the “Existing Warrants”), by reducing the Exercise Price of the Existing Warrants to $0.5855 per share.

The Warrant Amendment is subject to, and shall be effective upon, the consummation of the Offering and the Holder’s satisfaction of the Purchase Commitment. In the event that either (i) the Offering is not consummated or (ii) the Holder does not satisfy the Purchase Commitment, the Warrant Amendment shall be null and void and the provisions of the Existing Warrants in effect prior to the date hereof shall remain in effect.

Except as expressly set forth herein, the terms and provisions of the Existing Warrants shall remain in full force and effect after the execution of this letter and shall not in any way be changed, modified or superseded except by the terms set forth herein.

From and after the effectiveness of the Warrant Amendment, the Company agrees to promptly deliver to the Holder, upon request, an amended Existing Warrant that reflects the Warrant Amendment in exchange for the surrender for cancellation of the Holder’s Existing Warrants to be amended as provided herein.

[Signature Page Follows]

IN WITNESS WHEREOF, the parties hereto have caused this agreement to be duly executed by their respective authorized signatories as of the date first indicated above.

OUTLOOK THERAPEUTICS, Inc.

AGREED AND ACCEPTED:

Name of Holder: GMS Ventures & Investments

Signature of Authorized Signatory of Holder: ________________________________________

Name of Authorized Signatory: ___________________________________________________

[SIGNATURE PAGE TO WARRANT AMENDMENT AGREEMENT]