Getting late student loan payments off your credit report is a smart idea. You can challenge the timeliness and accuracy of the loan's payment history by sending disputes. If the lender is unable to get verification, the dispute will succeed and the late payment(s) will be removed.
If you're wondering what will happen if you don't get them off, consider this: 90 day+ late payments will hurt your score for seven years. 60 day lates will hurt for three years. Both will drop your score up to 100 points.
There is no guaranteed way to remove late payments from a student loan, but you do have options. Working with a professional is the fastest way to get them off.