Acquire Movement in A Crystal Cave
The rules are clear.


  Whenever you enter a Crystal Cave room, you become exhausted while wandering its maze-like passages and cannot use any more Boots this turn. You may still be able to move by Teleporting (described in Advanced Maneuvers), but you won’t be able to use Boots until your next turn.


(Emphasis mine)

A Crystal Cave doesn't cause you to lose unused boots; it prevents you from using any for the remainder of the turn. That means all boots on cards and Secrets played during the remainder of the turn are ignored, and so are boot gained on acquiring cards from the Dungeon Deck. You simply can't use them.