AVENGERS ASSEMBLE!: At the beginning of your turn, give any number of friendly characters power actions. For each one given, remove an ID card attached to this resource and place its ID Character adjacent to the character given the action. This game, that character is no longer an ID character, can't ignore pushing damage and returns to your sideline when it takes damage.

Does this removal of each ID card cause the ID cards to be scored?

Yes. Anything removed from the game is scored unless something tells you not to.