Upon the System upgrade, all individual quests were terminated.
All of the sudden quests, berserk quests, and also killing intent quests were erased as if they weren't there in the first place. Rex was bummed about this—as he lost a lot of rewards from that, but there were still quests that remained active.
One of them is the Kingdom Quest that he triggered back then.
He wanted to purchase the Vortex Pit of Elements, but it was too expensive for him.
Surprisingly, since this purchase involved the kingdom, or should he say, the empire directly, the System offered an alternative payment, which was through completing a Kingdom Quest to kill a Minor Chaos Inbrid.
Rex told Prof. K and Giana to complete this quest.
It seems like they succeed.
As it was not an individual quest, this quest remains even through the System upgrade.
I don't know why the System wants to kill the Minor Chaos Inbrid, but who cares?