The move reminder can only reteach certain classes of moves:
- Moves that the current species has on its level-up learn list (and, in generations other than 7, the level it learns that move at must also be lower than or equal to its current level). Eevee and most stone evolutions shift into a much different learnset after evolution, but the reminder only looks at the current species. If there's a move that the pre-evolved form has on its list, but its current form doesn't, that move will not be included. However, Sword and Shield universally changed the movepools of everything like that so that if the pre-evolved version could learn a move that wasn't otherwise accounted for, that move would be added as a level 1 move on the evolution so that this was no longer an issue.
- Moves that are in the "Relearn Moves" field. This field was only introduced in XY, and can only ever be populated for Pokemon that were met in those games or later. There are a few ways to end up with relearn moves:
- Hatching from an egg will set the relearn moves to whatever its moveset was when it hatched. Thus, if you can get an Eevee egg to hatch with a move like Baton Pass that its evolutions don't get as mentioned previously, it will be in relearn moves and you can get that back even after evolving. More relevantly, if it hatched with any egg moves that the species can't get any other way, you can replace those moves without worrying about being locked out of getting them back.
- Event distributions in XY or later also put their starting moveset into the relearn moves. Often this moveset will just be a regular list of level-up moves it would have at that level, in which case it's pretty meaningless, but doesn't hurt. Some events come with special moves, such as Happy Hour, and in those cases the fact that they're in the relearn list is relevant. You will be able to get those moves back later if you delete them at some point to make room for other moves.
- Omega Ruby and Alpha Sapphire have the DexNav feature where you can come across Pokemon that sometimes have special traits about them, and one of those possible traits is getting to include a random egg move in its list of moves. If this happens, the Pokemon will be given a single relearn move, with the egg move showing up there but the rest of its moves won't (they're all normal level-up moves, and can be learned by the reminder anyway, unless a subsequent evolution scraps those moves from its list).
- All Alola games have the Island Scan feature, where you can find Pokemon that don't appear in the region by any other means, and each species you can find this way is guaranteed to come with a particular one of its egg moves (assuming it has any possible egg moves). Unlike the DexNav case, Island Scans fill out the entire starting moveset into the relearn moves list, not just the egg move.
- In Sword and Shield, there are items called Technical Records (TRs) that essentially bring back the single-use behavior that TMs used to have in early games, as TMs became reusable items starting in Black and White. Each Pokemon keeps track of every TR that it's ever been taught, and the move reminder can be used to get back any of those moves it's forgotten so you don't have to use up another copy of the TR to get it back (in fact, the game won't even let you use a second copy of the TR on the same Pokemon).
If a move doesn't fall into one of these categories, the reminder is no help. In particular, TMs used to be possible to pass down as part of an egg's starting moveset, back when they were single-use items and many of them were only obtainable once per save file (so that you could plan carefully and get more mileage out of them), but this became unnecessary after TMs became reusable, and in particular it is not possible to do this in any game where the Relearn Moves field exists (although some species have egg moves that overlap with TMs they're compatible with, and in those cases the moves can still pass down to the egg).
In short: It is not possible to have a Blaziken wind up with Hone Claws in its relearn moves in any game, so if you delete that move after it's no longer a TM, you won't be able to get it back.
