Rated 5 out of 5 stars

Please, make it possible to remove Firefox button entirely - I just don't need it at all.

This review is for a previous version of the add-on (1.1). 

If you want to "remove" the Firefox Button, unfortunately, you did find a wrong extension here. Anyway, you may simply use userChrome.css to hide it:
/*hide the firefox button*/
#appmenu-button, #appmenu-toolbar-button {display:none}