Yeah. When you login to characters that have old event quests, I think you can technically do anything that hasn't been removed (like use sparklers or kill delve bosses), but can't complete any task that has been temporarily removed from the game.

Since the Jester's Festival quest-givers only appear during the event, there's no way to turn the quest in. If it's a character you won't need the quest log space for, you should be able to keep it and turn it in during the next event (assuming they don't revamp the event), or you can just remove it from your quest log.