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I would not specifically acknowledge the legitimacy of the debt.
I would contact them and state that you are willing to negotiate simply to resolve the issue.
If your negotiation position is an offer to pay in exchange for their agreement to delete their reported collection and they accept, you obtain both elimination of any debt and removal of the collection from your credit report, and thus from scoring.
I would begin by making a PFD offer. It can be for whatever amount you deem appropriate.
do not call them to negotiate do not pay them. Check your DM
Robert gave you wise counsel.
One thing not mentioned: when is SoL? Surely your leverage, and thus amount of offer, will be affected knowing this date.