TM Case appears in 4 version groups since Generation III, a Gameplay item in the Key Items pocket
PokéAPI item 550 of 2,223, Gameplay category, Key Items pocket
Effect, in PokéAPI's words
TM Case: “Holds TMs.”
Stores TMs and HMs.
Games
TM Case is listed in the text of 4 version groups, first in Generation III
Game index by generation
IIIIIIIVVVIVIIVIIIIX
Named in
EmeraldFireRed and LeafGreenLet's Go Pikachu and Let's Go EeveeSword and Shield