How can I hide this icon in Firefox? View -> Toolbars -> Customize doesn't work, because if I restart Firefox, it comes back.
Check for an extension with this name in Tools -> Add-ons manager and disable it (you can also open it by typing about:addons in the Location bar).
Per comment below, this answer should include information on how to hide the button without disabling the extension. Add this line to userChrome.css and restart Firefox.
Please also notify firstname.lastname@example.org of the problem so they can fix the behavior of the icon re-appearing after restart.