While I can't cite the specifics, almost every UL standard I've seen refers to two principles: mechanical damage and strain relief. A simple plastic bushing, or a chase nipple, would suffice to protect these wires from being damaged by rubbing against the hole. Being internal to the enclosure, I don't think there's a need for a strain relief fitting- though a "romex" connector might provide that. Since this is already installed, the easiest thing is to install a plastic bushing, by first cutting one side.
Is that a black, red & white #12 entering? If so, I guess the "green wire" wouldn't fit thru the hole. Also, what's in the handi box, and what size is it?? (Possible fill problem) Definite red sticker job> John