D&D 5e Greater Restoration Mechanics, the Undead, and the Soul

A little backstory: My group is campaigning into a village that has been usurped by a peasant wielding a jar that "collects" souls to power a Lich’s phylactery and it is almost full. The item is cursed and the wielder of the jar becomes corrupt carrying out the Lich’s plan, to be resurrected from his chamber inside of a Tomb. The lich promised the peasant that if he were to fill the jar, he would have the power over life and death to save his dying wife. The town and it’s citizens have been corrupted and twisted into the undead by the use of the jar.

The jar is homebrew, as I could not find a similar plot device that made sense mechanically or how souls would react to being bound in a high-power magic item.

One of my players (Dragonborn Barbarian) is world-reknowned for his birth-power of a Greater Restoration spell 3/day on his right hand. (rolled in his background).

He has the idea of using his magical ability on the undead (currently unaware of the jar or how the undead came to be).

I was wondering what I could do to make the role-playing aspects of this awesome for his character but also how would the mechanics make sense? Would the soul be denied to return to it’s undead corpse because of the magical restraint of the jar or would the undead explode or mutate into something more sinister? Does the spell have any effect at all?

My main question: What happens if Greater Restoration is cast on an Undead creature, given these circumstances?