For the グレた and グレてない in the Regi Trio's mini-bios, I'm assuming it refers to them behaving like delinquents, at least from Regigigas/Machia's perspective. It's possible further posts from this artist's series will clarify this, but the full series has yet to be uploaded and translated (in fact doing that is what I'm working on right now), so this is just my best guess with the information I have now.