I need to remove this or update it.
It does not show in the menu section and is not editable through the BeEditor
What you are referring to is the action button. Please go to Betheme -> Theme options -> header & subheader -> extras and change the action button. See here:
We sometimes also add the 'BUY NOW' button as the last menu item, be sure to go to Appearance -> menus and check there as well.
If the demo is a newer one, it also might be placed in the Header template made with Header Builder.