You should enter the amount you actually paid during the tax year. In TurboTax, you can enter the Form 1098-T as given to you and right below Box 2, there should be a link that says What if this is not what I paid to this school. When you click that, it'll bring up a new box where you can enter the amounts actually paid to the school. This means all amounts paid on behalf of you regardless of who made the payments.
Please see attached screenshots showing where the link and new box will be.
