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Without knowing the exact details of your situation I cannot answer your question with total certainty but assuming that the late payment is for a smaller account and not your current mortgage, I strongly believe that you will be fine and that your refinancing will close on time. First, if a lender checks your credit report prior to closing, they usually do that before you sign your loan documents so your lender would have already reviewed your credit report prior to this issue arising. Your lender is unlikely to pull your credit report again during your three day right of rescission period. Second, it usually takes at least 30 days for a derogatory credit event to appear on your credit report so even if the lender decides to check your credit today, they are unlikely to find the issue on your credit report.
While I do not think this issue will affect your refinancing, there are a couple of precautionary steps you can take if you are concerned. First, contact the creditor and try to resolve the issue. In many cases a creditor will waive a credit issue, such as a late payment, if this is your first negative incident with the creditor and you resolve the issue immediately. The second step that you can take is to prepare a brief, factual letter that explains the reason for the credit issue, outlines the steps you took to address the issue and states that the account is now current. Hold onto the letter unless the lender asks about the issue. If the lender asks about the issue, provide the letter to the lender to quickly address the matter. If the lender does not ask about the issue, do not raise the issue or provide the letter and your refinance should close as planned.
Again, I believe it is highly likely that your refinance will close without any issue but it is always good to be prepared.