Anyone know anything about booting regulations?

I work in a shop adjacent to a store which owns a large parking lot. Unfortunately we, along with the other stores in the area, don't really have parking lots (just some spaces in the back, not particularly clear or easy to find). That being said, anyone who parks in that parking lot has been booted relentlessly, within 1-2 minutes of parking in the area. The booting company set up camp in the corner of the parking lot, and boots anyone who does not go directly into the store. This has been going on for months, even before that store has opened, and since it was an empty lot and the store was closed, anyone who parked there was booted immediately. Cases include people walking into our store and inquiring about parking, and walking back out after we tell them to find their car has been booted. One case even involved someone stepping out of their car to use the atm on the lot corner and being booted for it. My question is, is there a time limit before they are allowed to boot your car? Is it legal for them to boot a parking lot for which there is no store open? Can they claim that they know for sure you were not going to go to the restaurant that owns the lot after say, getting a bubble tea from our store which is next door? Thanks for the help!

Edit: The location is Austin, Texas. Sorry about that! Edit 2: I don't know if this helps, but there's not a specific fee specified by any of the signs either