You can complain to the manager, he might take it off the bill. There were a couple threads last week where some people didn't have to pay for parking. I think it was a fluke in each case.
The first person said they didn't get charged, probably an oversite by the front desk. The 2nd person said they spoke to the manager and he said there would be no parking fee. We didn't get an exact reason why, maybe the manager was in a good mood.
Those who stay for a week often complain and get a deal of some sort, but none of this is written down, it just happens based on who you talk too.
The HRH lot fills up, so you could complain that you couldn't find a space and had to park over at the PBH. In fact that's what I tell many to do because that's a covered garage. You would park over there, and take a shuttle back to the HRH.
So there's a few reasons for you to use when complaining to a manager. I'd try the lot is full approach and you want the fee removed. This is all done by the front desk. But don't let it ruin your trip if you strike out. Stock the cooler before you arrive to save money. We bring two coolers with us. Lots of work carrying them up, but drinks are very expensive, so it's worth it to pre-game in the room.