This comes down to a matter of permissions. If this is a system dashboard you may need the ability to edit a system dashboard and you'll want to make sure you're not in personalize mode.
The easiest way to figure this out would probably be to create a temporary role and add yourself to that role. Then modify the permissions for that role so you're not changing large groups of users permissions trying to get this as you want it. See the screenshot below for where to find the System Dashboard edit ability.