I had my own issues with a vehicle return in Iceland and I can tell you it worked out fine although it was quite distressing initially (and EXPENSIVE for something that I truly believe was a shakedown of pre-existing or non-existing damage). You will pay for the damage at the point of return. You’ll then open a claim with AMEX and have to request some documents from the rental car agency. If Avis is anything like the rental car company I used, they will send all the information to you in Icelandic. AMEX will send the paperwork out to be translated. About 2 or 3 weeks later it will come back and you’ll get reimbursed by AMEX. I hope you took lots of pictures. With any luck all of this will be completed before your AMEX bill is due.

You can always dispute the charge, in fact I did do this after the rental car agency had not replied for my multiple requests for information, but ironically while I was on the phone disputing the charge I received an e-mail back from the agency with the requested documents. Once I was reimbursed I cancelled the dispute.