Interesting. Is the hotel claiming that you signed a registration card agreeing that they could charge your credit card for wear and tear to the room? If not, I think it is a deceptive practice for them to try to charge your card for an act of negligence. Let's say I buy a sweater from the GAP and pay with a credit card. On the way out, I accidentally walk face first into a glass door and shatter it. Can the GAP charge my credit card for that damage, since they have my credit card number? No.

If the hotel thinks you damaged their property, they should send you a letter asking you to pay, and if, you don't, they should sue you in small claims court if they think it's worth it. Giving a merchant your credit card number and authorizing a specific charge does not give that merchant the right to then charge that card for other amounts that the merchant thinks you owe them.

I think you should demand that they remove the charge, and if they don't, just dispute it with your credit card company. Unless you signed something saying "I agree that my card can be charged for damage to the room" (and it's possible you did) I think your credit card company will support you.

If the hotel had contacted you and requested that you pay for the damage, I think ethically you should pay a reasonable fee for the damage. Once they try the underhanded trick of charging your credit card for unauthorized amounts, I don't think you ethically owe them anything.