Here is what happened, I applied for a truck last summer and was approved at 17% on $14,000 with Wells Fargo I was able to refinance this past month with Open Road Lending for 11% I knew I would have a small drop because of history. Here is the issue...I had a payment due around the time the loan processing started, they told me I could pay it or not because they would be sending Wells Fargo a check for full amount. I decided to let them pay the total...well, what I didn't realize was by the time I got things mailed, apprroved etc it was over 30 days. Wells Fargo marked my debt paid off but the LAST PAYMENT was 30 days and was noted on the account. I am not sure what I could try and do, I was doing great building my score up.
You may want to head over to the rebuilding forum and ask them about Goodwill letters and similar strategies. The bottom line is that you made a late payment and you don't have any rights to have it removed. If you can get the lender to feel sorry enough for you, then they can opt to delete it. The folks in the R forum may be able to help you on how to phrase it, how to comport yourself on the phone, etc.
A contributor named Brutal Body Shots knows quite a bit about this sort of thing and may be able to help you.
Bear in mind that getting lates removed can take a good while (many months) with repeated attempts/requests, so you may need to cultivate patience and persistence as you consider how to proceed.
You don't mention an immediate need for a good score -- the way you describe your situation is more like a general desire to build a good score over time. If so, that's good, since as I say late removals can take a while.