Star check could be similar to "flight check" which is a callsign used when the FAA sends a team to check out an airport. I heard them at Shemya , Alaska and at Grantley Adams airport in Barbados. Flight Check checks out the navaids, ILS's etc. to be sure they are working and complying with regs. Star Check could be checking out arrival patterns or STARS.
Could be??? Dont know for sure.
Regards to All
"In God we trust, All others we monitor"