Ignobles mirror match

The situation is ignobles vs ignobles. One of the player has itty critters and uses critter cube on their opponents betrothed. What happens when they draw that betrothed? It is still “owned” by the original player so if they play it and pass it, would it’s ability not work for the critter cube caster? How would you know when you drew the opponents betrothed rather than your own? Would the card need to be somehow marked?