@Paula1843 When your credit card information is used fraudulently, it isn't the entity where those fraudulent charges were made that deals with it, it's the fraud division of your bank or credit card company.
My wallet was stolen and charges made for online purchases. It wasn't the places where the charges had been made that were responsible, and I certainly didn't deal with them- I called my bank to report the stolen card, and as fraudulent charges had been made, they then transferred my call to their fraud division, who could see the name of the online pay site the charges were made through, and they took whatever action they take in these cases. It took a few weeks, but the money was credited back to my account.
Airbnb should certainly be made aware of it, and the person who booked with your stolen info should been banned, but Airbnb really has no way if knowing if someone who calls them and reports this is telling the truth or not. I could call them to say it was a fraudulent booking not made by me, and demand they cancel it, simply because I wanted to get all my money back without being held to the cancellation policy of a listing I had in fact booked.
They are just a listing service, they aren't law enforcement officials or fraud depts.