You can always uninstall everything and make it look as stock as possible. They won't and shouldn't restore for you without your consent
That's what I did when I had to have my speaker replaced.
I tried to hide my JB and they didn't notice and just swapped out the faulty part.
How does one "hide" a jb? I brought my old 4s in for repair and they said they couldn't because it was jailbroken according to the Settings app.
The only thing is if they are nitpickers, they could update your OS to iOS7 before handing it back.
Uninstall mobile substrate and hide cydia somewhere (inside a folder, last page, etc). Uninstall the more well known jailbreak apps that aren't based on mobile substrate (ifile, terminal, etc)
It was probably the tweak's preferences that showed up in settings app that gave it away
No it was under General, About.
general -> about doesn't reveal anything about jailbreaking (as far as I'm aware of). Unless they had assumed you were jailbroken based on your iOS version
If it was a 3GS, then it might have been because the modem firmware (baseband) was 6.15.00