Pizza is a poor choice — it combines salt, fat, cheese, and usually garlic and onion in the sauce. A tiny bite of plain crust won't poison your bird, but pizza as a food should be avoided.
Keeper's noteIf your bird snatched a crumb of plain crust, don't panic — just offer water. But pizza isn't something to share. Skip the cheesy, saucy, and topping parts especially (garlic/onion).
What to watch out for with pizza
Pizza stacks up several parrot problems at once: a salty, fatty cheese layer (dairy), refined-flour crust, and a tomato sauce almost always seasoned with garlic and onion — both toxic to birds. Toppings add more salt and fat. No single bite is likely fatal, but nothing about pizza is good for a parrot.
How to serve it
Best avoided; at most a tiny piece of plain crust edge.
Never the sauce (garlic/onion), cheese, or toppings.