Could the Jets show interest in any of the players out there? While it's unlikely they will receive a compensatory pick in the 2015 draft, it's not impossible so if they were going to add another veteran, waiting until June does make some sense. Do remember though that any players released by their previous teams (Santonio Holmes for example) or re-signing with their previous team do not affect the compensatory pick calculation anyway, so the June 1 deadline isn't really relevant to them.
It's worth taking a look at which veterans are still available. PFT's "all-unemployed team" contains seven ex-Jets. See if you can guess who they might be before you click the link. (Clues: Six of them are offensive players and Kellen Winslow and Ed Reed are NOT included).