You say "Mother list child as dependent on her now Head of Household tax return and Mother paid for most of expenses through the year". We'll start by assuming that's true (even though the student has $23K + $11K = $34K of income and $24K of scholarship (scholarships are actually ignored in the support calculation).
Since box 5 of the 1098-T exceeds box 1, the student has additional taxable scholarship income ($13K +/- and maybe $17K, see "loop hole" below). This can be reduced by entering the book expenses. A space to do that will come up after entering the 1098-T, on the student's return, and following the interview. Room and board and travel are not qualified expenses and are not entered.
There is a tax “loop hole” available to claim an education credit, for the parents of students on scholarship. The student reports all his scholarship, up to the amount needed to claim the American Opportunity Credit (AOC), as income on his return. That way, the parents (or himself, if he is not a dependent) 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 conditions of the grant are that it be used to pay for qualified expenses.
Using an example: Student has $10,000 in box 5 of the 1098-T and $8000 in box 1. At first glance he/she has $2000 of taxable income and nobody can claim the American opportunity credit. But if she reports $6000 as income on her return, the parents can claim $4000 of qualified expenses on their return.
Books and computers are also qualifying expenses for the AOC. So, extending the example, the student had another $1000 in expenses for those course materials, paid out of pocket. She would only need to report $5000 of taxable scholarship income, instead of $6000.
The IRS actually encourages use of this technique. From the form 1040 instructions: “You may be able to increase an education credit if the student chooses to include all or part of a Pell grant or certain other scholarships or fellowships in income. For more information, see Pub. 970, the instructions for Form 1040 and IRS.gov/EdCredit". PUB 970 even has examples of how to do the “loop hole”.
Q. Lastly confirm that the 1098-T needs to be entered on the Childs return only.
A. Since the student is a dependent, she cannot claim a tuition credit, But the parent can (in this case using the loop hole). In that case both the parent and the student will enter the 1098-T, with adjustments. The student to report the scholarship income and the parent to claim the tuition credit.
Or is the parent's income too high to qualify for a tuition credit? If so, can the student claim the credit (using the loop hole)? Yes, in this case, because of the $2200+ tax bill. Technically there is a provision that allows a student-dependent to claim a federal tuition credit. A full time student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit (AOTC) if he/she supports herself by working . She cannot be supporting herself on student loans & grants and 529 plans and parental support. It is usually best if the parent claims that credit.
But, if the student actually has a tax liability, there is a provision to allow him to claim a non-refundable tuition credit. But then the parent must forgo claiming the student as a dependent, and the $500 other dependent credit. The student must still indicate that he can be claimed as a dependent, on his return. This is worth up to $2500 (AOTC shifts to all non refundable)
