Much ado about less than nothing.
But, if OP wants to pursue it, he ought to ask the car service for something reasonable such as 30% first.
On two bit stuff like this, Amex typically eats the dispute depending on how much it values the customer. But, it does a good job of keeping track of this stuff and there comes a point where Amex figures a customer isn't worth it.
This and the phone thing won't likely do the trick, but it will take OP close enough.
Me, I'd hang on to these chits for things that I care about a lot more.