Yes, you’re correct, the excess is taxable. It’s a common scenario, unfortunately, where billing is in one year and scholarship payment in another.
According to IRS Publication 970, Tax Benefits for Education,
“A scholarship or fellowship grant is tax free only to the extent:
· It doesn't exceed your qualified education expenses;
· It isn't designated or earmarked for other purposes (such as room and board), and doesn't require (by its terms) that it can't be used for qualified education expenses; and
· It doesn't represent payment for teaching, research, or other services required as a condition for receiving the scholarship.”