As far as I know, when any lender see a collection account in the credit reports, even though it says, "Paid as agreed with zero balance", it is a neg mark in it which reduce points in the score. So the best thing to request is to DELETE from the credit reports: "I will pay your company the amount of $xx as payment in full for the full satisfaction of this account.Upon receipt of the above payment, your company has agreed to DELETE this account and all previous notation of delinquency from my credit reports." It will be more effective.
Cesar