Short answer
Can a goodwill letter remove a late payment?
Sometimes. A goodwill letter asks the original creditor, not the credit bureau, to remove a late payment that was reported accurately, as a courtesy. Creditors do not have to agree, and some never do. It works best when the late payment was a one-off, you have paid on time since, and the account is in good standing. Keep it short: own the mistake, give the reason in one or two sentences, point to your on-time record, and ask for the specific month to be removed.
Paid once. Editable DOCX and PDF. Not legal or credit advice.