If you are turned down for a card and the letter explicitly states it's because of a judgment, lien, or repossession on your Equifax report, and you are certain this is not true because 1) you have never been sued 2)you checked your report after the credit card inquiry and there is no such entry there nor should there be, what would you do? I don't even care about the card anymore, but I was turned down for something that's not true.
You might send a letter stating that you had reviewed your Equifax report and found no such item. Request the Equifax report file number, and a copy of the part of the report showing those items that led to your application rejection. Will you get any answer? Who knows? They might give you the BS that they can't give that to you because their contract with Equifax prohibits it. This would be illegal under FCRA, so you could then file a complaint with your state AG, if it is worth your time. If other companies make similar claims when you apply, you may need to see an attorney about actions you can take against the CRA.
Under the law you are entitled to a free credit report due to being denied credit. You should take this report, and send a copy to the credit grantor who turned you down. You have the legal right to question the denial, if it is due to a sppecific item stated (as in your case it appears). It is possible they simply made a mistake, or the wrong CR was sent/reviewed. Before the letter writing, call the grantor (with a copy of your CR in hand), and speak to someone. Approach this professionally, I'm sure there's a reasonable explanation.