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I am sure others will weigh in but that offer is pretty solid. I say that because I work part time during Xmas season at Kohl's and this same offer would come up for some customers during checkout and i never saw one denied it may be only $300 credit limit but at least it is something. Secondly, Kohl's is backed by CapOne so they are pretty solid and it is a way to get your foot in the door for your dream wallet.
Their co-branded cards have different underwriting. Of you received a pre-qual, youre not blacklisted with the kohl's. You can try to pre-qual on Cap1's site also if you want to see if they have you early forgiveness.