Celiac fact of the day: It is estimated that any more than 20ppm (parts per million) of gluten can damage a Celiac's intestines.
That means if you have one million crumbs in something, and twenty of them are gluten, it will can make a Celiac sick. That is about 1/64th of a teaspoon!
I usually explain that if you can physically see a crumb of a gluten product, it will make me sick (crumbs in butter, mayonnaise, on a knife, on an unwashed plate, on the counter, in the toaster...). It doesn't take very much to make me very sick.