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Probably not. Just to be safe why dont you just go to a register and buy a stamp for .44 cents and get cashback then take it to guest services for your payment?
Well, if you have a checking account, why not just pay the bill through your bank's online billpay? It's usually free but it depends on your bank. Or...go the old fashioned way and write a cheque
I've made debit purchases with a PIN at Target stores. You probably can do it that way. Cashback limit is $40, but I'd imagine they could take an ATM card for bill payment.
It is possible to pay at the store with a debit card. I have done it here in Virginia.
I use to make payments at target every Month. You can make your payment in the returns department with cash or debit.