Friday June 4, 2021 @ 5:30pmCT - While packing our luggage, waiting for the Midway airport Budget to check-in the two rental cars in the lane next to us, suddenly our rental car was driven away. I attempted to flag it down, then immediately approached the Budget garage attendant to report that we had not been checked-in; he informed us not to worry, a receipt would be emailed. Still unsure, we immediately walked into the Budget glass office inside that garage just a few feet away and explained the situation again to the Budget employee sitting at the desk; she also informed us not to be concerned and that we'd receive an emailed receipt. No email was ever received. Monday June 7, 2021 - Called Budget to report our experience. Rep said they could "tell when the car was moved" to confirm return-time. I was put on hold, then the rep said our account looked "unusual", something about rental agreement numbers not matching, he needed to forward our case to another department, and to wait for an email. Received email shortly thereafter with final invoice showing an overcharge as an additional rental day had been added; return time 11:51pmCT. Proof: Our baggage claim tickets show a check-in time of 5:53pmCT. Our flight to California departed Midway @ 6:50pmCT. We landed in California at 8:51pmPT, which is 10:51pmCT. I have documents to prove all of the above, however Budget refused my request . We also have credit card charges showing gas station and a restaurant inside the terminal, as well as Google report showing time of Googlemaps used to airport and time of Southwest App used at Midway airport.