I have trouble rekilling this one unless I have overwhelming "firepower." A parrot released at the beginning of the game can steal you blind. The lightning reeds you would think could do it don't. What if there were an add-on one-shot plant that stands atop an existing plant shooting arrows? Or is there a plant food upgrade already doing it and I just don't know.
Moved because this is about It's About Time, not the original.
Well, it's a Bungee Zombie in all respects. Probably some of the strategies that work for it (having offensive plants behind other plants, ignoring low-cost losses, or having dummy targets) could work to Zombie Parrots as well.
Dummy targets are not very functional though, since Zombie Parrots can pass through plants to get any target. Winter Melons can barely deal with Zombie Parrots, though an amount of Peashooting plants can do well against Zombie Parrot.
I once had a zombie parrot carry a squash without getting squashed.
It was trying to steal my twin sunflower then I placed a squashed behind it and as soon it gets near the parrot, the squash went with the parrot.