Synchrony Bank Credit Card Complaint

Synchrony Bank Credit card department,

Unsolicited issuance of credit card Maryland

Yesterday, I went shopping at Gap store. When I checked out, the cashier asked me if I would like to receive an extra - % off. I said yes and she asked me to type my birth date, SSN and annual income. I handed in my state ID and my - credit card to her, and later she told me it 's done. After I received my receipt, I realized that I paid with another card ( gap card ). What a -!? I did n't even know it is a card, even a credit card. How can she do that? Is it like a fraud? I did n't even have that card in hand ( which was not issued yet ) and activate it. After this, I did some researches online and I realized that this has already affect my credit score. I am a foreigner and I do n't know much about credit card things yet. I felt that was totally a lie/fraud to me. Now I just want to 1. pay the full bill. 2. Cancel the card without affecting my credit score. Thank you very much and hopefully hear from you soon.