Washing a stainless steel rack is actually not done. Real pitmasters and chefs heat the BBQ properly, place their grill over the fire and brush with a wire brush. Which wire brush? The Bastard's brush, of course.
This long brush has a handy handle and an extra long handle, so you don't have to burn your hands on a hot BBQ. So, toss aside the notion of washing, and embrace the ritual of grilling mastery.