No, payoffs of credit card debt are not involved in your tax return at all.
If the debt was originally incurred to buy something that was deductible, like business supplies, you would have deducted those expenses at the time of purchase, so you have already benefited from any tax deductible purchases made with your credit card. Paying the card off later is a cash transaction that does not have anything to do with your return.
If you can isolate the interest you pay on a credit card to just business related purchases, you could deduct the interest on your Schedule C for self-employment, otherwise the interest is just nondeductible personal interest.
