Rental Car Towed

Hello all. My rental car got towed and the rental company does not seemto be in a rush to retrieve it. I went to the towing company twice to try and get it myself, but they wouldn't hand it over to me. The rental car company claimed they sent the necessary paperwork to the towing company for them to release it to me, but the towing company said they did not receive it. The rental car company number I called said they'd check with the branch to get it sent again and get back to me within 30 minutes. They never did, and their office closed shortly after. My flight home was a couple hours later so I put the keys in the rental car company's drop box. My concern is that the rental car company will charge me for the extra time the car remained at the towing lot (despite me trying to retrieve it an hour after it was towed). I assume they can leave the car in there for days and rack up fees and then pass those fees onto me... So I am curious if anyone has had any similar experiences or advice for how to handle this? Do I need a lawyer? Do I file an insurance claim? Any help anyone can provide would be greatly appreciated. I am very worried.