Shar037:
Okay I understand now. Unfortunately, this all boils down to you're not sure if you were late and they (supposedly) are. You cannot get them removed on this basis. It was worth it to try at first but now you've been told. If you want to continue to dispute, and I think you should, you need to get proof that you are correct.
You said Great Lakes took over the loan and the original servicer reported it as late during the transition? If that's the case, Great Lakes *should* have your complete from your old servicer....but I personally had no luck with that. You might want to call and speak with a specialist; my servicer had to do a request for them to look in a warehouse of files, and gave me an estimate of 120 days (it only took a few weeks). Whatever you've got to do to get them, if they even exist. During transitions it's not rare for the servicers to drop the ball and you will be held responsible. Another helpful too is to do the requests in writing, fax or mail, with no phone number given. They will have to reply in writing. If they find them, you have your answer. If they don't, you have a paper essentially saying they can't verify the lates.
If you cannot get far with the credit bureaus, the next step is the Ombudsman. Some find solutions with them. I had a lot of success with the Consumer Financial Protection Bureau though. They take your complain and send it to the servicer. Mine was unusually helpful after that. Emphasis that they verify the lates without proof if they don't have your account information at the time). Names, dates, times , and copies of correspondence and bills are helpful.
As far as your current statements from Great Lakes, just keep at it however your due date doesn't change and your payments should be stay abut the same. If you're late you're liable to be held responsible. Nothing you can really do about that except what you're doing.