Advice needed on security Deposit Not Returned: New York

I publish illustrative scenarios prepared by my practice. All participants and conversations are fictional. The fictional posts are not posts by real users, accounts of client experiences, or reports of actual results.
Illustrative scenario prepared by my practice.
For informational purposes only. This is not legal advice. Laws vary by jurisdiction. Consult a qualified attorney for advice specific to your situation.
Hypothetical question

I've been trying to resolve this in New York on my own but I'm stuck.

lease says no pets but ESA rights. I've been dealing with this for about 2 weeks now and the situation isn't improving.

I have been renting for 8 years. My monthly rent is $3,887. I have a written lease.

Do I have a strong case? What should my next steps be?