GitLab has asked you for the wrong thing. The format of a counter-notification is specified in 17 USC 512(g)(3), which requires, among other things:
A physical or electronic signature of the subscriber.
"The subscriber" in this context refers to the person who originally uploaded the content (i.e. you personally). It has nothing to do with the copyright owner.
However, in the comments, you have indicated that the item in question is the Yuzu emulator. Yuzu has not previously been challenged under section 512 (as an unauthorized copy), but under section 1201 (as a circumvention technology), which is an entirely different provision of copyright law that is not subject to counter-notices (but, confusingly, is sometimes also referred to as "the DMCA" because it was enacted at the same time as section 512). If your clone of Yuzu was removed as a result of a section 1201 claim, GitLab can and probably will ignore any counter-notices.
GitLab should have provided you with a copy of the takedown notice, which should clearly identify the basis on which the notice was sent. If it alleges "that the complaining party has a good faith belief that use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law," then it is a section 512 notice and may be counter-noticed. If it alleges that the repo can circumvent technologies which "effectively control access to a copyrighted work" (or any similar language), then it is a section 1201 notice and may not be counter-noticed.
Finally, please be aware that a section 512 counter-notice requires you to provide personally identifiable information sufficient for the complainant to file a copyright lawsuit against you, and to consent to the jurisdiction of the United States over such a lawsuit. You should be prepared to defend such a lawsuit before you file any counter-notice. It may be wise to consult a copyright attorney who is licensed to practice in the United States before proceeding.