Landlord still wants pet rent after I gave them my ESA letter.

Renting a 1BR, and I have an ESA. I got an ESA letter through RealEsaLetter a few weeks ago and submitted it to the leasing office with my accommodation request. They accepted the letter but are still saying I owe the standard pet fee plus pet rent monthly, same as anyone with a regular pet.

My understanding was that an assistance animal isn't treated as a pet, so pet fees and pet rent shouldn't apply the same way, but I honestly don't know if that's still accurate or if I'm repeating something outdated. I also don't know how long they're allowed to sit on the request before giving me a written answer.

For anyone who's been through this: did your landlord drop the fees once you pushed back? Did you have to send anything beyond the letter itself? And is there a point where it's worth filing a complaint?