Edwards, acquired last season from Cleveland, signed the tender worth $6.1 million -- which would have required another team to give up first- and third-round draft picks to New York.
Running back Leon Washington chose to not attend the workout, and is one of New York's four restricted free agents who haven't signed their tenders. Washington, a fourth-round pick in 2006, received a second-round tender.
Agent Alvin Keels said on Twitter that Washington, a Pro Bowl kick returner in 2008 who's recovering from a broken right leg suffered last season, will weigh his options while rehabilitating.
Keels added that Washington's rehab "is going great" and is expected to be cleared for running drills within the next two weeks and be 100 percent for training camp. Washington, given a tender for $1.759 million, is looking for a long-term deal.
Recently signed linebacker Lance Laury was the only other player to not attend Monday's workouts as he prepares to relocate after spending the last four seasons in Seattle.