No. There is a power to impeach judges for any reason, or no reason. That is legal. That is a power of the legislature.
It's not about impeaching Greer.
Who's gonna impeach Jeb if he imposed his power to keep Terri alive?
The issue is whether Jeb, as an executive, could use his power to engage a check in one particular case on the power of the judiciary. It would be the ultimate power play, and risky politically, but I haven't seen anything that suggests it would be illegal.
In other words, the day should rightfully come when a governor or even a president, acting legally, uses his political might to impose his will upon the judiciary. The most effective checks and balances are driven by the will of the people, not by black-robed tyranny.