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Zombie doesn't pick up the egg because its been added to the blacklist: `/zombiescantgather zombie add minecraft:egg`
This time I got the `/zombiescantgather piglin` command output in the screenshot!
Tracked zombies holding glow ink sac (what an unfortunate example lol). Purge button to try to kill them all, refresh button to refresh the list, and teleport buttons to teleport to any of the mobs.
Adding an item to the Zombie blacklist with a command suggested by the add button. Items can be removed with the red X buttons.

Prevent Zombies from picking up certain items!