At a minimum, I would ask for receipts to document the actual cost of repairing / replacing whatever was damaged. $500 is a very arbitrary number. It sounds like a rough estimate of the damage cost.

I am also very curious about the nature of the damage. Is it something that would have been common for an occupant to do or is it vandalism or something? Would there have been noise when the damage occurred? This might be helpful to your case depending on specifics.

If you have honestly been wronged, you need to decide how much it matters to you. Your best course of action might be to just grin and bear it. Amongst other things, SPG could pull your platinum status if you make too big of a fuss, but if you are OK with that, and you are willing to spend some time and energy fighting for the principle here, you have a number of options:

1. Credit card dispute. Should happen immediately.

2. Social media pressure (here, TA, Facebook, etc., etc).

3. Small claims court. File in your home state and name the hotel GM as a defendant personally.