Well, your credit gets "soft" inquiries all the time. That's what all those offers come from. If you read them, the fine print will say something like "subject to credit approval." That's because they didn't actually pull all your info (your whole credit report for review), they just saw your 3 digit number and sent you an offer. Now, if you actually applied for one of these, you would authorize a "hard" inquiry, just like getting a mortgage or car loan. Soft inquiries do absolutely nothing to your credit; they don't even register as events. So no worries about all those offers.