Momentary dip. It recovers after a few months as long as you aren't doing anything else to mess up your score like not paying bills. I guess some people love those perfect credit scores but honestly anything over 750 is fine for most things even getting a mortgage.
A chargeback should be (I would imagine is required to be, but haven't checked) free. If the company wants to roll the number too then fine, but that should be just inconvenient not a cost.
If your credit card company is charging you, leave them.