I know how to remove that entirely but not piecemeal.
I've also managed to break it sufficiently to show nothing when they are clicked.
However the security options won't affect the rendering of the actual buttons hence i abandoned the idea of using them and moved the locked down area to another menu that didnt display the activity centre...ie the standard tree on the left.
The way to do that is to not use your "root" from within the 'manage' top level menu, but rather push it to something like "home" or even give it its own custom menu.
If you want people to have access to right click computers then you will have to put them into an Altiris OG and show that in the custom menu. Once you break down the permissions to see too few things the activity centre becomes a waste of empty space and just looks terrible, you are as well creating it 7.0 style.
So really the below screenshot might be not what you want but it might do what you want.
Does this help or answer the question?