Go check the MCC, which you can see by going in as if you were going to dispute the charge. Click the little chevron on the left and in the details for the transaction it'll show what the parking vendor's MCC was.

If it was enough money to be worth bothering, Chase may give you the points/credit manually. I stayed at a hotel in Japan whose MCC was something weird but the business name was ABC HOTEL on the statement. It was a couple grand, so I SM'd for my points and they gave them to me. Same issue with several restaurants, but not worth my time for 15 points here and there.