No, you don't need to put the $556 on her return. It's not enough to change anything.
But, here's the real deal: you have between $855 and $2135 coming from the IRS. File an amended return and claim the American Opportunity Tax Credit (AOTC), i.e put the 1098-T on your tax 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 (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 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.
Using your numbers: Student has $3098 in box 5 of the 1098-T and $2542 in box 1. At first glance she has $556 of taxable income and nobody can claim the American opportunity credit. But if she reports $3098 as income on her return, the parents can claim $2542 of qualified expenses on their return.
The $3098 added to her $8890 wages is still less than the $12,200 threshold for having to pay any tax.
