With the follow up information I think the original few poster's ideas on responses still work. The complaint was still one your could acknowledge and emphasize with and then provide a solution (pay here, ask for reimbursement, directions to correct lot, etc.).
Reminbursement is not possible because the parking pass specifically stated exactly where to park at. Plus we were told that those parking passes were only valid at the parking garage stated on the pass.
The parking attendant let her know that her parking permit, which she took a picture of, was not valid at the parking garage both of us were working at. He let her know which garage she had to go to, and her gave her directions, but she did not want to go to that garage. She told both of us that we should have let her park at the garage we were working at for free and that he should have accepted the picture of the parking permit she took using her cell phone as proof. Neither were possible.
So what do you do as employees when you 1) tell a customer where to park at with their parking pass, 2) give them directions, 3) the customer tells you that they should be able to park at the parking garage you are assigned to even though the parking pass specifically states where to park at, 4) the customer tells you they do not want to go to the parking garage where the parking pass is only valid at, and 5) they will not pay for their parking?
What do you do? You reiterate policy, empathize with their frustration, reiterate policy again, and tell them they have two choices; pay for parking at your lot, or return to their designated lot.
Are you asking what to do if they refuse to take either of those options and are blocking the entrance for other (paying) customers? The answer in that case is to ask your supervisor how they'd like you to handle it. They may prefer you call them, security, or go straight to the cops.
If you're asking how to magically make a frustrated customer un-frustrated and compliant, I'm afraid there's no such solution. There will be people who are unhappy. Sometimes there will be nothing you can do to make them less unhappy, either because they're unhappy for an irrational reason, or because they may have a legitimate gripe for which there is no solution. Here's the good news: It is not your job to make everyone happy.
It is your job to provide accurate information, to be courteous/give good customer service, and to take payment for cars in your lot.