A lot of companies try to get you to use their system like Navan or Concur but see if you cant buy on your flights on your card. Figure out what the "to the airport policy is."
A lot of companies pay for your time and transit to the airport. I worked a deal that i wouldnt submit those reimbursement for exchange to park in short term parking. Such a difference tbh. If they wont allow it, my other suggestion is just to uber. There's nothing worse than getting off a flight in February at 9 PM at night at 19 degrees and getting on a shuttle for long-term parking.
If you are flying out of SLC, I would strongly suggest avoiding flying home on Thursday nights during ski season. Its a disaster. Also Monday mornings can be a pain as they are flying home.