Depending on your card issuer, you ought to be able to do a partial chargeback online and not even have to waste the time on a call. Few, if any, card issuers will actually investigate. For that amount, they will simply pay out the $10 and be done with it.
If it isn't worth the 45 seconds sometime when you are online anyway, go ahead and drop it.
Do be aware that you should hold until you have flown the ticket. There are carriers which get snarky, believe they are right and insist on an add/collect or cancel your ticket.