The credit is based on what was paid to the school.
That should be in box 1.
If you paid 10,000 in December 2019, that will be included in Box 1
If the scholarship for that period posted the next year in 2020, subtract that amount from box 1 and don't count it as income for 2020.
Keep good records using the 1098-T and the students yearly statement.
"Refunds received after 2019 but before your income tax return is filed. If anyone receives a refund after 2019 of qualified education expenses paid on behalf of a student in 2019 and the refund is paid before you file an income tax return for 2019, the amount of qualified education expenses for 2019 is reduced by the amount of the refund."
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