This answer is fairly late, but I would suggest you let them know they can file a dispute on their credit card, but they have a limited window of time to do so. They should log into Airbnb website & it should show that they cancelled and that a Refund is being processed. I have taken screen shots of that page as documentation, as well as keeping the emails Airbnb sent me about my refunds. The site doesn't let you "print" pages on their site, but you can do Control/Shift/S & save a png from the page showing on your screen.
FYI, it's been nearly 60 days since I filed a dispute, and I STILL haven't gotten a refund of my larger $$ reservation, despite submitting the afore-mentioned proof. I suspect Airbnb wants to hang onto my money (or my bank's money, really, since they issued me an immediate temporary credit.)