If they are really bad, like with burn't cheese I soak them in the sink and then scrub them with a brillo pad and try not to bend the screen in doing so. Pizza screens are mostly associated with New York style pizza.
Mine do not get that way very often unless I let my son make the pizza, he is a bit more "creative" with where the cheese and sauce lands. Also they tend to not do as well with "cursed" frozen pizza. Shall I use the word "Totinos"? My son, college student, makes these on my coveted pizza screens and invariably they stick big time.
Former Pizza restaurant owner confession--- We "rarely" cleaned the screens, just used them over and over. Those little pieces of crust caught between the metal flaked off after a few more pizzas got cooked on it at 550 degrees in a bakers pride gas oven.