Surprise - it's a subtitling error! The first four characters (完全被甲) certainly mean "full metal jacket" (in the sense of a bullet with a full-metal jacket). But the last two (混乱), which seemingly went untranslated, mean "confusion" or "disorder"... or, perhaps, "Panic". You know, as in Full Metal Panic!.
So, what does Full Metal Panic! have to do with anything?
I have a pretty good guess: episode 9 of Full Metal Panic? Fumoffu features the cast visiting a hot springs resort. Once there, some of the men (led by military man Kurz) attempt to spy on the girls in their party as they relax au naturel in the open-air hot springs. Like Junichi's friends in Hajimete no Gal, Kurz-and-co's efforts are indeed foiled by rather tight security. I suppose this was a homage of sorts.