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.

about a 1/2" of scotch 33 would work. what?

I would have used a 1/2" chase nipple.Would also break the ends of those screws off that the box is mounted with(there is already enough places in a panel to get cut or scraped without adding to it)

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