Should the difference between out of state tuition and NEBHE tuition count as income / get reported on box 5 for form 1098-T?

Q. Should the difference between out of state tuition and NEBHE tuition count as income / get reported on box 5 for form 1098-T?

A.  No, except if the the tuition it covered is also reported in box 1. Be sure it wasn't. 

Scholarships are tax free if they pay for qualified expenses (tuition, fees and course materials).  Since this program is specifically a waiver of tuition, the benefit (regardless of what they call it, scholarship, grant, waiver, remission) is tax free. Ask the school what's going on. That sounds just plain wrong to me and they should no better.

In the 1098-T screen, click on the link "What if this is not what I paid the school" underneath box 1. Add back the offsetting tuition that the waiver covered. 

The 1098-T is only an informational document. The numbers on it are not required to be entered onto your tax return. However receipt of a 1098-T frequently means you are either eligible for a tuition credit or possibly your student has taxable scholarship income. 

You claim the tuition credit, or report scholarship income, based on your own financial records, not the 1098-T. In the 1098-T screen, click on the link "What if this is not what I paid the school" underneath box 1. You will then be able to enter the actual amounts paid. You will also reach a screen that allows you to adjust the scholarship amount for "amounts not awarded for 2021 expenses".

Or if you find it easier, just change the numbers in boxes 1& 5 to what your records show. The 1098-T that you enter in TT is not sent to the IRS.