Simple analysis - without looking at the comments.

They associate your license-plate with your card at time of parking card issuance. Later they associate the car with a location by automated scanning (which I have seen them do).

A bit of software sorting and searching, and from two duples, a triple: car, plate, location.

Then you make it a quadruple - car, plate, location, credit card ID. :-)

Now - to read and see if I matched the consensus.