At first glance, you only have $711 of qualifying expenses for the tuition credit (because scholarships paid most of the tuition). But if the student declares some of the scholarship as taxable income, the parent can claim a bigger tuition credit. This is what TurboTax has done (apparently). You should be getting a $2500 credit ($1000 on line 29 of form 1040 and $1500 on line 20).
She is reporting $3289 as taxable scholarship income. That is not enough to generate any tax on the federal return but apparently does generate tax on the state return (I'm not familiar with NY rule details). For whatever amount of NY tax she is paying, you are getting $1789 more, on your federal return (2500-711= 1789).
You can reduce some of the tax, if you have some book and computer expenses to enter.
