[California] ESA fee due on lease start date

Location: California

have been offered a lease agreement for a no-pet policy from a realtor who manges more than 4 properties, and that lease includes a flat $750 cleaning fee, not a deposit, for the presence of a legitimate ESA that abides by the latest rules set out by the state of CA, i.e., a recommendation from my doctor who I've been seeing for more than 30 days, not some website where I pay $50 for a phony letter. Is this fee legitimate to include? It's a cat that weighs less than 10lbs. If I sign this agreement, am I boned with no chance to recover the fee amount? She did mention that I may be passed up for the next applicant on the basis that they do not own pets.

Any and all responses will be greatly appreciated. Muchas gracias.