Try to go to View -> Toolbars -> Customize. This will open a new window, but the entire Firefox window behind it will change so everything is draggable. Just drag that pencil into the window that appears, and the pencil should disappear. To re-add the pencil, just drag it from the list in the window to the same place.

Thanks for the try RIC. However, the stupid pencil is not draggable with either left or right mouse. And I have searched hi and lo on the internet with no success in finding it.

List your add-ons in a reply. On the Help > Troubleshooting Information screen, click "Copy all to Clipboard", then paste into the reply area. This way, maybe someone can identify which add-on is putting the icon in your status bar. See: http://support.mozilla.com/en-US/kb/Using+the+Troubleshooting+Information+page

There is an add-on to re-arrange items in the status bar: https://addons.mozilla.org/en-US/firefox/addon/1759/