(A) How many pizzas were uneaten at the end of that day's lunch.
Correct, if there are significant number of uneaten pizzas at the end then school can save good enough money by reducing the number of pizzas ordered, in that case conclusion will be shattered.
(B) Whether pizza provides the same level of nutrition as a typical cafeteria lunch.
Irrelevant, we are already given in the argument
"A vice principal was exploring cost-reducing measures that would not compromise nourishment" so we have it at the face value, thus, this option doesn't help us.
(C) Whether another Italian restaurant in this town would provide a similar deal and offer free delivery.
Irrelevant, we are already given in the argument
"he concluded that the school could not save money by replacing a day of cafeteria lunch with a day of pizza from this restaurant.", thus, this option doesn't help us.
(D) Whether other, more expensive dishes from that Italian restaurant, would provide a more balanced and varied set of nutrients.
Irrelevant, we are already given in the argument
"he concluded that the school could not save money by replacing a day of cafeteria lunch with a day of pizza from this restaurant.", thus, this option doesn't help us.
(E) Whether the faculty preferred the pizza to the typical cafeteria lunch.
Irrelevant, it doesn't matter what's the choice of faculty as Vice Principal is already making decisions.