If the damage is less than $200 and did not involve another party then you will be given an option to pay for the damage up front with no administrative fee (e.g. If you got a dent on the door because you were pushing a shopping cart and lost your balance then you can pay for this up front. However, if that dent was caused because another vehicle brushed up against the door then that will have to go through claims). If you choose to pay up front then they will bill your credit card and that will be the end of it. If you decline to do that or you deny the damage then you will fill out an vehicle incident report and it will be handled by Hertz Claims Management where various fees will apply. HCM will work with your insurance company but any portion not paid by your insurance will be your responsibility. I don't think they are allowed to charge your card at this point in time.

Like all other things, you can refuse to pay but they will report it and it will show up on your credit report. If the damage is significant then I would expect them to take you to court.