You said "If I understand correctly, the classes were valued at $500 each and were awarded pre-tax"
What that usually means is she got a tax free benefit. As such, you claim nothing on your tax return, as your tuition was paid by a tax free grant.
But I think you meant to say that she received an after tax benefit, meaning she had to pay tax on the benefit ("her take-home pay was reduced by around 500 * 25%-ish tax bracket"). What that means (usually) is that $500 was added to her W-2 as imputed income. So, effectively the tuition was paid by her after tax income.
You have no income to report on your tax return. You can claim the tuition credit, on your tax return, because the tuition was paid with after tax money. Educational expenses is an exception to the rule that you must have paid the expenses to get the deduction. You may count tuition paid for by your pard's after tax money. You count the $500 paid (not the $125).
