Those are hardcoded menu items. We currently don't have a UI to control their display. The only way to hide them is to use CSS and hide their element. The below CSS should hide the two menu items you're wanting to remove.
Code:
.cbMenu_UE_MENU_EDIT,
.cbMenu_UE_MENU_VIEW {
display: none !important;
}
The problem however is it's going to hide those on your profile too. So the best way to hide them on just other users profiles is to use CB Auto Action and the before or after profile display trigger with a Code action to add the CSS conditionally. You'd check that the profile user id does not match the viewing users user id using the below condition.
[user_id] Not Equal To [cb:userdata field="user_id" user="#me" /]