Clark: I'm not gonna let who ever did this hide behind their badge.
Chloe: If we're gonna sneak you across this thin blue line, Go undercover?

you're gonna need something a lot
more substantial than just a press pass.

'The thin blue line' is a standard expression that refers, a touch poetically, to the police.

ie They wear blue uniforms. They are a thin line protecting us from criminals.

Thanks, Clive!