Since you did not get reimbursed for the spring and fall semester, you can claim the spring and fall semester tuition for the tax credit.
Q. Can I modify the 1098-T?
A. Yes. The 1098-T is only an informational document. The numbers on it are not required to be entered onto your tax return. You claim the tuition credit based on your own financial records, not the 1098-T. Just change the numbers to what they should be. What you enter is not sent to the IRS, only the calculation results.
That said, it doesn't make sense that they would reimburse the summer session and not the fall. If you are expecting to be reimbursed for the fall, in 2023, you do not count the fall tuition for the tuition credit.
