I've been dealing with credit report issues for decades. As a general rule, unless a borrower can demonstrate that the creditor has violated the law, or that the account was actually paid according to the contract, there is no relief from a negative credit report entry.
That said, I have had some success with literally negotiating the negative entry off of a credit report. A creditor has the power to delete a previous entry on grounds that it is a "clerical error." This raises no issue with the credit reporting agency (CRA), because it is an admission that the original entry was erroneous, but for a harmless reason.
The problem that I have encountered is usually due to being unable to reach an employee of the creditor who has the authority to negotiate. That is, there are employees who deal with accounting, with negotiating foreclosure issues and bankruptcy -- but, there is almost never anyone with a job description that includes the adjustment of a credit reporting error -- because, as a general rule, credit reporting information is automatically transferred to the CRAs.
Credit card issuers routinely adjust credit report entries. Some issuers even use a one-time adjustment for late payment as an card holder benefit for marketing purposes. But, loan servicers don't do this sort of thing, because there's no market benefit.
What this means is that you need to find someone in authority with whom you can "make a deal" And, by "deal," I mean, "offer to pay them for the cost of having an employee remove the account entry. There absolutely is someone at the loan servicer who can delete the entry, and there is also a manager somewhere who can negotiate a deal with you. But, finding that person can be near to impossible. You just have to keep trying.
One option is to write a letter to the CEO of the organization. The letter will inevitably be read by the CEO's administrative assistance, and if he or she thinks your sufficiently "needy," there is a good chance (in my experience), that the assistant will mention the issue to the CEO, who may say something like, "I don't really have time for this sort of thing, but if you think the borrower should get a break, then call [middle manager name] and have them fix the credit report.
It's a power thing, and it makes the CEO feel more in touch with the "little people." And, it gives the assistant some power, which makes him/her feel special (without giving them a raise).
The bot***** *****ne is that there is no "legal" means to enforce the issue, because as a matter of law, your payment was late, or insufficient. So, you have to do what lawyers do when the law isn't on their side: try to negotiate a deal/settlement -- because that's all you can do.
Note: If there were a legal means of adjusting your credit report, I would tell you, because I've knocked dozens of these types of issues off of credit reports in the past. But, your facts just don't provide an legal leverage -- so, negotiation (or, pleading with the gods) is the only available route.
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