Cookies are sugar, fat, and refined flour, and chocolate-chip varieties are toxic. They're junk food for parrots — a plain crumb is harmless, but not something to offer routinely.
Keeper's noteWatch for chocolate chips above all. A plain shortbread crumb on rare occasion is harmless; a healthy bird treat (millet, fruit) is always the better call.
What to watch out for with cookies
Like cake, plain cookies aren't poisonous but offer nothing nutritionally, while loading sugar and fat. Chocolate-chip cookies contain cocoa (toxic), and many cookies include raisins, nuts, or spices of varying suitability. The default should be 'no'.
How to serve it
At most a plain (non-chocolate) crumb, rarely.
Never chocolate-chip cookies.
Choose millet or fruit as an everyday treat instead.