The primary way to delete late payments from a credit report is to dispute them if they are inaccurate or erroneous. Legitimate, accurate late payments usually cannot be removed and will remain on the credit report for up to seven years. However, if the late payment was reported in error or is related to fraud, it can be disputed and removed upon verification. Steps to remove late payments from a credit report include:

1. Review credit reports from the three major credit bureaus (Experian, TransUnion, and Equifax) to identify late payments and assess their accuracy.
2. If late payments are inaccurate or erroneous, file disputes with the creditor and the credit bureaus, providing any proof or documentation.
3. If disputes are not resolved favorably, consider re-disputing with additional evidence or adding a consumer statement to explain the situation.
4. In cases of extenuating circumstances (e.g., medical emergencies, natural disasters), contacting the creditor to request goodwill removal of late payments may be possible.
5. For fraud-related late payments on accounts opened without consent, file identity theft reports and inform the creditor's fraud department to have the information removed.
6. If disputes fail, a formal complaint can be filed with the Consumer Financial Protection Bureau (CFPB) for assistance in resolving the issue.

Other methods like pay-for-delete agreements, where debt collectors offer to delete negative information upon payment, are generally not recommended or guaranteed to work. It’s important to note that accurate late payments generally cannot be removed early from credit reports but will diminish in impact over time. This detailed approach should help understand how and when late payments can be deleted from a credit report.