I can't recall them exactly, since it's been a while since I've seen Men in Black II and that movie was not the sort of experience I store in the favored areas of my memory, but I believe it was something to the effect that a bootleg neuralyzer would fry your brain inside your head if it didn't work precisely perfectly, and even if it did, the memories would be patchy at best for an undetermined length of time before everything fit back in place. I'd say that it would be best to find some way outside of the MIB movieverse to get the memories back, and even then, there should at least be a little time before their restoration to exploit the comedic and/or character-building potential of having one's mind erased, or the whole affair would be sort of pointless.

...bought all three MIB movies, I can probably find you an answer once I'm done marathoning the lot. Or you could, potentially, find something outside the MIB universe.

You would not want to do that. If there is any organization in the canons of the multiverse that will be fully prepared for unexpected and off-the-wall occurrences, it's going to be one that regularly fights off or contains the damages caused by aliens and monsters with such efficiency that the outside world at large hardly suspects of their existence. They might be able to sneak in, but they are probably going to get captured. Then the DIA will have to go in and clean up, which is likely going to cause an interdimensional incident since the main technology that the PPC uses to make people forget about them came from the very people that it would need to be used on, so they'll be able to tell what the signs of an altered consciousness are, deneuralyze someone, and find out everything. I suppose this could be circumvented by going outside science fiction and using a suggestion spell or Harry Potter's Memory Charm, but it will almost certainly be more complicated than that in execution, since this is still the PPC we're talking about here and the simple solutions rarely play out as intended.

Summarized: If your agents think that they will only be "in trouble" when they get back, they will be very unpleasantly surprised by what they'd really have to deal with. "In trouble" is if you accidentally leave a candy wrapper on the Black Pearl. "In trouble" is if you do a sloppy job unbolting Elrond's bed from the ceiling and he notices the hastily-covered holes. "In trouble" wouldn't touch this.

I like the idea of an Agent getting Neuralysed and having to Deal With It. Brb, filing it away for future arcs...

(It would totally suck if one of the E/C duo lost all memories of them being in a relationship. Which means this is an excellent idea that I should keep on file.)