Greg is a Watchdog and part of Lord Hater's army. His name was revealed in "The Funk", where he was given a wedgie.
As Commander Peepers was so quick to suggest messing with Greg specifically, it can be presumed that Greg is a recurring target of their juvenile antics. He seems to take it moderately well, as he stopped noticing his wedgie when Lord Hater slouched off screen.
In order to help Lord Hater get out of his funk, Commander Peepers tried to do a lot of things to cheer him up, including giving Greg a wedgie. However, it still didn't cheer Hater up, which causes a frustrated Peepers to drop Greg, who's wedgie is still on.