I’ll cut to the chase on this post because this is a silly change to make between Gnome 2 and Gnome 3. If you add a shortcut launcher to the panel in Gnome 3 (classic mode), you will find that a simple right click doesn’t show “remove”.

If you want to remove a launcher from the panel in Gnome 3, you need to press the alt key and right click the launcher. You should then have the ability to move or remove the icon.