As a general rule, Poke-league gym leaders do not use HM/TM moves in badge battles. Badges are supposed to be a test, after all, not an insurmountable challenge, and this way the challenge is more standardised. The only exception to this is gym leaders that hand out a particular TM. They may choose to use this particular TM move in battle to show challengers what it is capable of I.E. Bugsy, who hands out the TM U-turn, may also decide to use U-turn in battle.

Note, this mindset only applies to regular league challenges. Leaders of non-standardized gyms (such as the Aurora leagu) may have different rules, which is best checked with each individual.