Go into the People App. Click on the person that you want to remove from the widget (really, you are removing them from Favorite People.) To make it easy, you can go along the bottom to the icon with a silhouette profile with a heart on it; these are your favorite people.
While you have the contact that you wish to remove open, click menu. Click "Remove" from the menu and they will be removed from Favorite Contacts, and, hence, the widget.
