I perform judgment acquisition and recovery. You do have a few options.
You could try to settle with that credit card company. Yet, if they already know that you're trying to refinance, then they might try to play some hardball sensing an opportunity for a pay-day relatively soon. Another option is to work with someone like me (a neutral third-party) who'd buy the judgment at a discount, and settle with you also at a discount (which you'll pay off before you close on the refinance). (We make the spread in between.) Another option is for you to work with a debt consolidator to help you to consolidate those 2 judgments into a single loan (for which you'll need to agree to go onto a payment plan), and they'll help you to remove those liens.
You could also ask them to agree to subjugate their lien behind any institutional financing (hence the refinance), or risk getting nothing at all if your lender forecloses on your property.
Keep in mind that each option has it's own set of caveats.