The Jets are playing hardball, not because they worry about Zach and him being released.
But because when they sign Mekhi Becton (or someone else) to a deal in a few years, they can point to the team leader and say "See, everyone gets it. No exceptions".
Could be Becton, could be Maye, could be someone else. Although Becton (as a huge human being with serious potential for injury or weight issues) is actually a great example of someone who you might worry about giving a big long term deal