Without knowing the exact details of your situation I cannot answer your question with total certainty but assuming that the credit issue is relatively minor and not related to your current mortgage, for multiple reasons I believe that you should be fine and that your refinance should close on time.
First, if a lender checks your credit report prior to closing, they usually do so before you sign your loan documents so your lender would have already reviewed your credit report prior to this issue arising. In the majority of cases, 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 in the unlikely event your lender decides to check your credit during the right of rescission period, they are unlikely to find the issue on your report.
Review What is the Right of Rescission Period for a Refinance?
While this type of issue typically does not affect a refinancing, there are a couple of precautionary steps that you can take if you are concerned. First, contact the creditor and try to resolve the issue. In many cases a creditor will waive an issue, such as a late payment, if this is your first negative incident and you address the issue immediately.
The second step that you can take is to prepare a brief, factual letter of explanation that outlines the reason for the credit issue, the steps you took to address the issue and states that the issue is now resolved. For example, if you missed a payment or had a late payment, the letter should note that the account is now current.
If the lender asks about the issue, provide the letter 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.
One point that I should highlight is that if the credit matter pertains to your current mortgage, this may cause more of a problem. For example, if your refinance lender learns that you missed your most recent mortgage payment, your refinance may be delayed or in a worst case scenario, potentially cancelled.
Unlike other types of debt such as a credit card or car, personal or student loans, the lender does not rely on your credit report to learn about possible issues with your current mortgage such as an account delinquency. If you missed your most recent payment, owe a late fee or your mortgage is delinquent, the refinance lender learns this information when your loan documents are prepared.
Depending on your lender and loan program, a late or missed mortgage payment within the past three months may disqualify you for the refinance. This is why, more than any other loan, it is always important to pay your mortgage on time throughout the refinance process.
Again, I believe it is highly likely that your refinance closes without any issue or delay but it is always good to be informed and prepared.
Mortgage Refinance Right of Rescission Period: https://www.consumerfinance.gov/ask-cfpb/how-long-do-i-have-to-rescind-when-does-the-right-of-rescission-start-en-187/