Hello, I am at the "Did you pay tuition or other higher education expenses" section. I received scholarships/grants that how covered those costs. So do I claim?

Maybe.

You are not required to enter anything there, even if your school issued a 1098-T. The 1098-T is only an informational document. The numbers on it are not required to be entered onto your tax return. However receipt of a 1098-T frequently means you are either eligible for a tuition credit or deduction or possibly your student has taxable scholarship income. 

Scholarships that pay for qualified educational expenses (QEE - tuition, fees, books and other course materials) is tax free.  Scholarship amounts that exceed QEE is taxable income, on the student’s tax return.

If box 5 of the 1098-T exceeds box 1, TurboTax (TT) will treat the difference as taxable income, unless you enter additional QEE at books and other expenses.

If Your QEE exceeds your scholarships, you (or your parents if you are a dependent) are eligible to claim an education credit or deduction.

There's even a loop hole available to claim the credit, if you are on scholarship. 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 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.