I got offers from Credit One and several other similiar card issuers a lot, and sometimes pay-day loans. I find this really annoying and insulting. Can you tell the credit bureau that you don't want these sub-prime lender's offers but green-light thoese from certain creditors, like Chase/Citi ?
And I wouldn't call getting subprime "insulting" There is no real intent. Merely that your credit profile meets (and exceeds) their very low standards. Opt out, or just throw away unopened the ones you don't want.
The reason their promotional offers are often for less favorable terms is that if they obtain your name from a CRA to make an offer for credit, the offer must be a firm offer.
That means that if you, upon applying and review of your full credit report, are found to meet the normal criteria they specified when obtaining your name and address from the CRA, they must honor the "firm offer."
A less than the best offer gives them legitimate room for denial if the consumer then specifies better terms in their app.