Do I need to declare in my taxes scholarship money refunded to me? Extra money that was refunded to me by the university after being applied to my tuition?

Q.  Do I need to declare in my taxes scholarship money refunded to me?

A.  Yes, but not exactly the amount "refunded to you". 

Scholarships that pay for qualified educational expenses (QEE - tuition, fees, books and other course materials) is tax free.  Scholarship amounts that exceed QEE is taxable income, on the student’s tax return. Room & board are not QEE.

Normally, if box 5 of the 1098-T exceeds box 1, TurboTax (TT) will treat the difference as taxable income, unless you enter additional QEE at books and other expenses.

You need to do the math to see if your scholarship exceeds your qualified expenses. Then, 

 enter at Educational Expenses and Scholarships, under Deductions and credits (not the income section). Answer yes to having education expenses and working on a degree, even if you’re not. That’s needed to get to the scholarship entry screen. Check received scholarship, grant or aid at the Did you have any of these common situations screen. At the scholarship screen, enter the amount of the grant. When asked if any was used for room and board (R&B), answer yes. Then enter the amount you calculated to be taxable, in the pop up box. R&B are not "qualified educational  expenses".  So, this is how you tell TT that it is taxable. You didn’t have to literally use the scholarship for R&B.  This will put it on line 8r of Schedule 1.

Even though you did not get a 1098-T (you qualify for an exception) you should look at this post on the five main points on the  1098-T (and the tax issues in education):

https://ttlc.intuit.com/community/college-education/discussion/re-what-do-i-do-with-form-1098t/01/3760212#M63114