Student Loan Garnishment and removal from credit report

My loan was in default and my wages have been garnished for the last 3 years. I have looked at the rehabilitation of the loan, but never had enough money to make the lump sum payment. However, I recently looked back at all my pay stubs to see just how much I have paid. I called the lender to see what my options were to get this out of garnishment. However, I am ~ 6 months away from paying it off, if I keep the garnishment, and it takes 9 months to have it rehabilitated.

The lender (NYS Higher Education Corp) said that if I kept the garnishement, that at the end, I would get settled debt letter and I could request that this is removed from my credit report...and that I would be eligbile for additional student loans. Is this correct? I assume that once its paid, my credit score will increase dramatically, right?

Thanks!