Actually, you would have to pay if you have a car - regardless of whether you have a annual pass that includes parking at the lots/garages. The annual pass doesn't include overnight parking anywhere and doesn't include parking at a hotel.
If you don't have a car, tell them you don't have a car. But, I'm pretty sure that the DL hotels (PP, GCH, and DLH) have a resort fee now (instead of a separate parking fee).