Self employed

You can put "Reimbursement of Fees" for the explanation.

You can enter the income as “Other Income” so it won’t be subject to self-employment taxes.  Follow the steps below:

1. Open TurboTax
2. Select Federal Taxes
3. Select Wages & Income
4. select Start by Form 1099-MISC under Other Come Income
5. Select Yes to Did you get a 1099-MISC?
6. Follow the prompts to enter your 1099-MISC
7. Enter the reason: Reimbursement of AMEX fees to Describe the reason for this 1099-MISC
8. Select None of these apply to Does one of these uncommon situations apply?
9. Select No to it didn’t involve work like your main job
10. Make your selection to How often did you get the income?
11. Select No to Did it involve an intent to earn money?

For additional information, review the TurboTax articles What's the difference between self-employment income and other income? and Where do I enter a 1099-MISC?