Simple answer: the parent. If the student is the parent's dependent, only the parent can claim the tuition credit.
The long answer is more complicated. The 1098-T is only any informational document. The numbers on it are not required to be entered onto your tax return. If you claim the tuition credit, you do need to report that you got one. However receipt of a 1098-T frequently means you are either eligible for a tuition credit or deduction or possibly have taxable scholarship income. You claim the tuition credit, or report scholarship income, based on your own financial records. Unfortunately that sometimes means working around the 1098-T and the TurboTax interview.
If her qualified higher education expenses (QHEE -tuition, fees and course materials) exceed her scholarships, you may count the net you paid, in claiming the tuition credit, on your return. However, if her scholarships exceed her QHEE (they paid for room & board too), the excess is taxable income and gets reported on her return.
There is a tax “loophole” available. The student reports all his scholarship, up to the amount needed to claim the American opportunity credit, as income on his return. That way, the parents can claim the tuition credit on their return. They can do this because that much tuition was no longer paid by "tax free" scholarship. You cannot do this if the school’s billing statement specifically shows the scholarships being applied to tuition or if the conditions of the grant are that it be used to pay for qualified expenses.
