I swiped my credit card once when I checked in at the hotel. I thought it was pre-authorization, so I signed it Then a week later, the hotel gave me another bill.

Pre-authorization can be revoked after you finally leave the hotel and check out. When I stay in a hotel abroad, I often use a credit card for pre-authorization, and then use a debit card to settle the bill. Credit cards do not generate fees. Of course, your hotel did not cancel the pre-authorization, and charged you two money. You should ask clearly when signing the bill. ...

It's no use telling the bank now. Banks only care about collecting money themselves. Call the hotel and get the money back.