My understanding is one shop pays expenses, but is not evaluating the parking. Why would the OP need to explain anything beyond telling them she does not need the reimbursement? Why would you think they would ask or beyond that, even care?
I don't know if it is mystery shoppers in general, but I am always amazed by the things people feel they need to explain whether it is why they want a receipt for their purchase or why they want to close their bar tab before moving to the dining room.
Equal rights for others does not mean fewer rights for you. It's not pie.
"I prefer someone who burns the flag and then wraps themselves up in the Constitution over someone who burns the Constitution and then wraps themselves up in the flag." -Molly Ivins
Never try to teach a pig to sing. It's a waste of your time and it really annoys the pig.