Yep so a tiny bit of the wrap wouldn’t hurt, but it’s not as healthy (of course) as the veggie part - exactly as it is for you.
So assuming you have lettuce, tomato, pepper.... maybe cheese and meat? And the wrap.... you want to avoid the cheese and meat, most people here will tell you avoid tomato although it’s actually not too dangerous it’s just acid-y. Limit the wrap part. That leaves lettuce and pepper...maybe add a bit of carrot and birdie has his own “salad” for dinner!