I had this happen to me once, but I flew immediately after dropping the car and therefore could produce boarding passes/other evidence of leaving. Still ended up charging the amount back though, because Avis decided they were still right. Credit card company saw sense.
Might be tricky if you didn't fly immediately. Do you have any evidence that you didn't need a car from that point? Did you stay in a hotel that offered zero parking options? With a companion that had their own car?
Also watch out for any erroneous 'damage' that appears in the extra days you 'rented' the car.
Failing that, showing you left on the 11th via a boarding pass might be enough for them to realise they were wrong and credit back all the days.