Thompson, the ranking Democrat on the House Homeland Security Committee, sent a letter to TSA director Edmund Kip Hawley on Wednesday discussing the worsening situation at the airport.
Last month TSA investigators came to Jackson to look into claims by current and former workers that TSA management used inside information to cheat undercover tests of security procedures.
The workers had also claimed that a lax attitude existed toward federal security relations that sometimes allowed dangerous items to pass through security.
Thompson said he learned that selected employees were the only ones interviewed by the investigators. Also the interviews took place in rooms adjoining the offices of Federal Security Director Larry Rowlett and other top TSA managers.
In a letter to Hawley last month, Thompson called for Rowlett to be put on administrative leave during the investigation to ensure employees could speak without fear or repercussions.
Citing Rowlett's long career in federal service, including time spent as chief Secret Service agent for Mississippi, TSA officials issued a statement of support for Rowlett.
On the grounds the letter involved personnel issues, TSA spokeswoman Sari Koshetz would not comment. TSA also did not comment on whether investigators have substantiated the claims made by current and former TSA employees.
TSA spokespersons, in earlier statements, denied any dangerous items made it past security checkpoints, instead suggesting that any warnings of upcoming tests were the result of workers at one airport gossiping with Jackson screeners.
Former TSA screener Bill Gillam said he was interviewed by two investigators at a location away from the airport.
Gillam and others claimed that TSA management briefed workers before secret tests that involved undercover agents attempting to sneak dangerous items into the airport.
Gillam said he also submitted a list of names of other workers willing to be interviewed about airport operation. Some of those people have not been interviewed, he said.