Eagle: Removing unwanted bits of copper pour
Uncheck the orphans property of the polygon.

From Eagle's General Help:


  Orphans 
  
  As a polygon automatically keeps a certain distance to other
  signals it can happen that the polygon is separated into a number of
  smaller polygons. If such a polygon has no electrical connection to
  any other (non-polygon) object of its signal, the user might want it
  to disappear. With the parameter Orphans = Off [default] these
  isolated zones will disappear. With Orphans = On they will remain. If
  a signal consists only of polygons and has no other electrically
  connected objects, all polygon parts will remain, independent of the
  setting of the Orphans parameter.