Did you travel on the same flight as your luggage? Your claim shack matches your flight number? If so, the airline will deliver your lost or delayed luggage to your residence, hotel, or office. Just check with the lost luggage agents at your airline carrier. As far as the parking, it is run by the airport and not the airlines so unless the airline gives you a parking voucher or token, then yes you would have to pay to park.
The airlines generally deliver luggage ti your house or hotel at no charge. Did you ask?
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