Premier Bank First Premier Bank Put me on credit report because I refused the card AFTER terms were disclosed. When applying online, no way to refuse Sioux Falls, South Dakota

I guess you missed not only the disclosures that came in the mail with the offer.  But the link to the terms and fees as the very first thing you see on-line when you start an application.

Now, as for any damage to your credit.  You will get "dinged" for the inquiry.  But this is very minor and the effect is very short lived.   None of the automatic credit scoring programs are even going to care that it is a closed account.  You may again get "dinged" a few points because it was a new line of credit.  However, like the inquiry that would be very short lived.  The only time after that it may remotely matter is going to be when your report is manually reviewed is for major purchases such as a house or car.  If it matters they would ask you to explain the issue.  But creditors are not going to automatically think "bad credit" when the account was opened and closed in the same month(or even within the next month). 

But if you are really concerned about it.  Then you may want to try and dispute it with the Credit Reporting Agencies.  There is a chance that since it is closed FP will not verify the account and they will just remove it.