Presumably the bill is on the credit card.

The only recourse is with the credit card company. State your case as best you can and hope they go to bat for you against the car rental company.

American credit card company..........American customer..........foreign car rental agency..........I don't think you'll have much of a problem.

Now, if they sent you a bill in the mail.........well.........you've got a fireplace..........correct?