"Ivy Token's" effect to inflict damage does not start a Chain.

If the "Ivy Token" is destroyed by a card effect, inflict damage after the effect resolves. If the "Ivy Token" is destroyed by battle, inflict damage at the end of the Damage Step, when monsters destroyed by battle are sent to the Graveyard.

If "Remove Brainwashing" or "Owner's Seal" is activated, control of the "Ivy Token" is shifted to the player that activated "Wall of Ivy's" effect.