I know there are a few games that put restrictions on HM moves, so I want to know which games and what restrictions. Please don't question my curiosity.
Edit: Don't answer using information from Bulbapedia. Different Bulbapedia articles say different things.
As far as I’ve played, no, there are no moves that the move deleter cannot delete.
But, in Pokémon emerald, the move deleter will refuse deleting the move Surf, when no one else in the team knows it. But as soon as you teach another Pokémon Surf, he will readily delete one of the two.