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. Since the tuition was mostly paid with taxable reimbursement (for tax purposes, YOUR money), you may use it to claim the tuition credit.
If you claim the tuition credit, you do need to report that you got a 1098-T.
When you enter the 1098-T in TurboTax (TT), leave box 5 blank. Lying to TurboTax to get it to do what you want does not constitute lying to the IRS. When asked if you got Tax-free employer provided assistance, answer yes and enter only $5250.
You state that 1098-T box 1 shows $24,000 but your employer only paid $18,000. When you enter the 1098-T, in TT, enter only $18,000 in box 1. At the 1098-T screen, in TT, note the link "What if this is not what I paid the school". You can change it using that link or just enter the right amount in box 1.
