Well, you can do it even much easier - just select the single point (that is not connected with another points), make sure that only the point is selected and not the whole mesh - and press delete. How to select the only point - first select the whole mesh and after click again - but only on the point - black dots on the mesh counter will disappear, showing only one black dot.
The same way you can delete connected points - make sure that only they are selected and press delete.