Care credit

I took out a care credit charge for my daughter for dental care. I received a few bills and gave them to my daughter to pay. She never got her dental work do e but the dentist was payed by care credit. I received. Letter fro a law firm in an attempt to collect a debt. I paid the bill and settled with the law firm. Now the dentist has the Money how do I do about retrieving my money from the dentist. Was told that they would have to send the money back to the bank nd then the bank would give me back that money. Can you give me an information about this. Have contacted the dentist and didn't get an answer back. The dentist has the money ho do I get it from them