In New York a construction lien release could be one of two things.
First, it could be a document that a contractor signs and submits along with an application for payment. A construction lien release in this sense is also known as a lien waiver. Essentially the contractor is telling the person that is paying that upon receipt of payment the contractor waives and releases the right to file a mechanic's or construction lien.
The second is a document that releases or discharges a mechanic's lien that has already been filed. Once the mechanic's (a/k/a construction) lien has been satisfied the contractor files the lien release/satisfaction with the property entity (usually a county clerk) and the lien is discharged.