No. You DO enter the 1098-T and claim the tuition credit for the amount paid. It does not matter that the money came from a trust. You claim the credit based on the 1098-T and/or the schools billing statements. The K-1 is irrelevant, for purposes of the education credit. This assumes your daughter is your dependent.
The K-1 is entered, in TurboTax, to report the earnings income, on your tax return (or your child's tax return, if the K-1 is under her SS#).
