According to the information provided, if the credit card was seven months overdue three years ago and was later paid off, but now the mortgage loan is shown as a bad debt, there may be the following reasons:

1. The impact of overdue records on credit history: Even if overdue debts have been paid off, overdue records generally remain on credit reports for a longer period of time and may have a negative impact on credit ratings. This will cause the lender to view you as a higher credit risk, which may affect your borrowing terms when applying for a home loan.

2. Bad debt information may have other reasons: In addition to overdue repayment records, other factors may also have an impact on the application of mortgage loans. For example, there may be other outstanding debts or other bad records on your credit report, which could cause a lender to deem it a higher risk and mark your loan as bad debt.

3. The impact of credit rating systems: Lenders often use credit rating systems to assess borrowers’ credit risks. Based on an individual's credit history and other factors, lending institutions may risk grade the loan application and make adjustments to the applicant's borrowing conditions. If you have a lower credit rating, it may result in stricter loan terms, such as a higher interest rate or the need to provide more security.

To sum up, late repayments will have a negative impact on your credit rating and may result in being marked as a bad debt when applying for a mortgage. In addition, other factors such as other arrears, bad records, etc. may also have an impact on the loan application. Before applying for a mortgage, it is recommended that you communicate with the lending institution and understand the specific reasons so that you can take appropriate measures to improve your credit situation.

Extended information: Credit record refers to the record of an individual’s credit behavior in financial activities and related information, such as loan records, overdue repayments, guarantee records, etc. Credit history will have an impact on financial behaviors such as personal loan applications and credit card applications. Credit records are mainly recorded and managed by the Credit Information Center of the People's Bank of China (Central Bank).

According to relevant Chinese laws and regulations, lending institutions can refer to an individual's credit record as one of the important evaluation criteria when evaluating a borrower's loan application. Therefore, maintaining a good credit record is crucial to personal financial activities. It is recommended that borrowers regularly check their personal credit reports to ensure the accuracy of their credit records and take proactive measures to maintain and improve their personal credit status.