My car got towed by mistake and the towing company is refusing to work with me on it

I live in an apartment complex in GA, USA. The lease agreement states that any vehicle that isn’t in a drivable state, whether that’s a mechanical or legal issue, can not be parked at the property. Every quarter, the maintenance department will scope the property and put a warning sticker of impeding towing, the reason why, and the expected date.

Long story short, they just did this about a week ago. My car, which is drivable in every shape and form, did NOT get a sticker. It’s my daily driver, so I rely on it to get me to and from work. Today I walk out to go to work and my car is gone and I noticed all the cars that had stickers were gone too so

I put 2 and 2 together and realized what happened. I called the front desk and the clerk told me it probably got towed by accident and to call the towing company.

Well, I called them and they want me to pay to get the car out despite the fact it was towed by accident. They want an insane amount of money for a car that’s almost 30 years old. I told them I can prove it was towed by mistake using the property-management’s records and they said it doesn’t matter.

From my point of view, this is theft. Do I have any real legal recourse or do I really have to cough up the $1500 to get my car out?