Hi Ty!
It's 'mar' from the other board (slight identity crisis a few years ago).
My favorite Fed story:
A few years ago I was a Metroliner PIC in a 121 passenger operation. When I was inside going over the paperwork I get approached by a Fed with an officious flip of her ID and a firm handshake.
She'd like to have a walk around the airplane prior to departure and I've got nothing to hide so I say, "Sure, help yourself."
So I finish up and it's time to load up the pax and I head on out to the plane. I meet my Fed at the base of the stairs and I tell her she's welcome to seat 1B (with a jack) and does she need headsets or did she bring her own?
She takes her seat. I take mine. And the FO is outside intercepting oversized carry on bags. It was at this point in time that she tap, tap, taps me on my shoulder and I turn around to see what she wants.
"There's an oil leak on the right engine."
"Huh? What?"
"I noticed an oil leak on the right engine when I inspected the airplane."
"We're boarding. Right now. The airplane has been preflighted. I'll talk to you about it when we get to the destination."
So off we go, land, off load the pax and naturally I'm hoping she just forgets her little oil leak thing. No such luck. She waits until everyone is off the plane and then says, "So...about the oil leak..."
"Alright. Let's go have a look."
I get to the engine. There is a sheen of oil on the cowling but give me a break. That's not a leak (drip, drip, drip) it's just an oily cowling. So then I open the inspection door and check the level. It's perfectly acceptable.
"Sorry ma'am, I don't see a leak."
"Ok, thanks for the flight."
What I learned from that experience (and naturally every situation is different) is that as the PIC you need to stay in control and don't let them push you around.
But not every Fed is a thug. Some are genuinely nice guys but in general my usual stategy is to approach them before they approach me. They are so accustomed to pilots avoiding eye contact and turning the other direction that I sort of get a weird thrill out of meeting their eyes, walking up to them with an extended hand, introducing myself and asking them, "What can I do for you?"
It totally disarms them.
Of course it helps if you're working for a good operation and you really don't have anything to hide.
Good luck!