You could completely uninstall Skype, and then reinstall it without checking the button, but there’s a simpler (and more geeky) method.
Removing Skype Extension Manually
The first thing you want to do is go into Tools \ Add-ons and disable the extension if you haven’t already. You’ll notice that there’s no uninstall option, which is rather irritating… Skype is very useful, but it shouldn’t pollute my Firefox.
Now close Firefox and open up a Windows Explorer window and browse down to the following location, adjusting if you installed Firefox somewhere else:
In that folder you’ll find another folder with the following name:
Just delete that folder (or move it somewhere else if you want to be safe), and then open Firefox again. You’ll notice that the Skype extension is no more.