Fallen for credit card fraud

Unfortunately, I fell for a well-done credit card scam over the weekend. In the evening I was contacted by the hotel where we had soon booked a room that I should provide a credit card for confirmation. I hesitated for a moment but the link looked good - all the data matched. Name, date for one night, amount of money, etc. (called the hotel on the phone, they probably have a data leak - that's all I know, they couldn't tell me more) So I quickly brushed my teeth and...