Q. Do you have to toivel a brush (the nylon threads are attached to a wooden handle by a strap of metal), that is used for covering bread and similar with eggs. oil and the like?

A. Poskim rule that a mivreshes or brush made from plastic materials does not need tevila (Hakashrus Kehalacha p. 288, Tevilas Kelim p. )
Horav Shlomo Miller’s Shlit’a opinion is that even if the nylon threads are held together with a metal strip attached to the handle, as they usually are, it does not require tevila since that part does not touch the food.
The Rov added that same would apply to a plastic frying pan spatula or turner with a metal handle.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a