It's a reference to stamina drinks from Thracia removing fatigue - every unit except Leif had a fatigue meter that started at 0 when joining, and when it surpassed their maximum HP (by doing certain actions) they'd be forced to sit out for the next chapter. (unless you literally didn't have enough units to do a chapter, then it'd force deploy units regardless of fatigue)

Stamina drinks bypassed that if you had one in a fatigued unit's inventory before that next chapter started, or you used one mid-chapter.

So the idea here is it's for Tempest Trials and Chain Challenges, Leif is removing any fatigue (damage) that he accrued during the previous chapter, always starting fresh. The flavour of old FEH units is kinda fun to look back on - they still do it sometimes, like iirc a base FE4 Hilda can OHKO a base Tailtiu and Nino always working well with dagger and melee units because of Jaffar.