Is it legal for a dentist to charge for services not rendered on a credit card when the dentist broke the contract and services were not rendered?

My dental provider got me apporoved for a credit card for impending dental work. The first appointment, I arrived to find the offcie locked. I called and they said the dentist had an emergency and I was rescheduled. When I returned a second time, another dentist came in, reviewed my xrays and literally walked out telling the dental assistant that the tooth didn't need extracting nor an implant. Even though no services were rendered and they broke the contract, they put the charges on my credit card and are refusing to credit it back.