Drag the Character prefab into a new scene.
Delete the 'Minimap Elements' GO. When informed that this will break the prefab, select 'Continue'.
Under the root Character GO, select Apply to update the prefab and remove the Minimap Elements GO from it. You will see it removed in the project view.
In the project view, change the name of the Character prefab to something else, say 'Char'. You will see the Minimap Elements reappear in both the prefab in the project view and the instance in-scene.

There appears to be no way to get changes to 'stick' when later changing the prefab in the project view.