Affiliate Marketing Secrets

I applied for financing for a medical procedure I want to undergo because I don’t have the money to pay it all at one time and prefer to pay it off little by little every months for the next couple of years.
The financing company says it will check the following:
“Information we receive from you on credit applications, driver’s licence, and other forms, such as your name, address, assets, and income;
Information about your transactions and experiences with us and our affiliates such as your account balance and payment history; and
Information we receive from consumer credit reporting agencies or other outside sources, such as information regarding your creditworthiness and credit history.”
I think I won’t have any problem for anything except..I am wondering about my credit history. I have one visa card only and I am doing ok. I am paying it off entirely practically every month.
BUT one time I went to shop at Sears and you know when they ask you if you want a HBC master card, I said fine. I never received that master card…just some other kind of plastic card (but it’s not written master card on it. I think it’s some kind of member card or something.) And I decided not to use it so I cut it and threw it in the garbage. I do receive letters now about that saying I have to pay..I guess some kind of service fee. Which I always ignored. Now I have been receiving phone calls too, which I ignored too.
Is this gonna show up on my credit check? The amount they want is like 130 dollars I think. It’s not a whole lot.