 At the conclusion of the season, Greene was the Devils' nominee for the Bill Masterton Memorial Trophy, awarded annually to the NHL player who best shows perseverance, sportsmanship and dedication to hockey.During the 2019–20 season, on February 16, 2020, Greene was traded to the New York Islanders in exchange for David Quenneville and a 2021 second-round pick.The move came following fourteen seasons with the club.