Complain to both Amex and the rentacar company. I had something similar-ish though much smaller issue (cleaning charge for vacuuming the interior, after a 2 week rental) and sent the complaint letter to both: ie, addressed to both and made clear that they were getting carbon copy letter since it was the same complaint.
Car company dithered, but Amex reversed the charges and said "rentacar can come back if they can justify it". That looks to have gotten it to a different level in the rentacar customer service centre, and an apologetic letter arrived some time long after. Belated happy ending