Every regional I have interviewed with including Republic had you fill out paperwork that gives them access to all your FAA records.

In a nutshell, they will get all your flying training records from previous employers for the last 5 years, anything that is in the National Driver Database (like habitual DUIs, Reckless driving, etc), and everything the FAA has on you. Medicals, pink slips or any action taken on your certificate. If you're worried about what they have, you can get all this information yourself before you interview.

Thats what you give them permission to do when you sign all the stuff in that big packet HR sends you.