Clearing out your Home page Recents

. . .  and the same is true for the Home Screen which is the question you asked.

As Glenn has described, you can't clear the list and start with a new one.  I believe the information is taken from the Operating System, and if you reboot, the greyed out list shown in Glenn's screenshot will not appear.  (Not sure about that.)  But once you restore a number in Preferences, the last used files will reappear.

EDIT>PREFERENCES