I had a student loan like 10 years ago, and it is since paid off completely and closed. However, in September 2009 and January 2010 I had late payments.
Is it possible to ask that they be removed? Or is it more trouble than it is worth?
The credit file is a history of your use of credit. It has the good and the bad info that covers a period of years.
There is a process of getting incorrect info either changed, or removed. But there is no procedure for getting correct information removed.
Lenders want to know your history so they determine if you generally pay your debts. They then look at your income and other expenses to see if you have the cash flow or the reserves to pay back the loan.
The decision to lend is based on those two analyses. Removing bad history would provide a false impression to the lender.
Now when you apply for credit the lender can decide to loan the money even if you don't have perfect credit. They may decide the risk is still good, or they could raise the rate, or they could lower the maximum they will lend.
Some lenders will allow you to submit to them a written explanation of any ding on the report. They do this so they can document their decision to overlook a few small issues.
Call your old student loan lender and ask. It's always possible, but in your situation unlikely.
The best time to have addressed this was before you had paid off the lender. Now that the account is paid and closed, there's little incentive for the lender to do anything.