Jones is a mediocre QB, i.e. he's a backup talent with only one decent season. The Giants have a lot of picks this year. That said their first round pick is 25, but in combo with other picks they could easily move into if not above the middle of the round. History has shown they can get a good QB in that range.
Time to tell Jones he has no leverage and move on in the draft. A good rookie QB can play as well or better than Jones has played. Jones is a mediocre RPO QB who hasn't mastered the more complex multi-read progressions of the NFL. Even without his contract demands it would be time to move on from this backup level QB.
Or they can get into the Jimmy G sweepstakes.