I'm finding this tool really buggy. If I drag out a plane, all it's control points are intact, if I then command-drag off another plane, then delete it, the original plane losing some of it's control points. The same happens if I undo also
In vanishing point, when selecting a plane in a multi plane grid and pressing delete: the plane visually disappears but the remaining grids act like the plane is still there: the corresponding anchor points are gone, and the remaining grid may not be altered as though it is still attached to the deleted grid. Upon exiting and re-entering vanishing point the deleted plane is visible again.
Because of this there is no way to delete a plane once created, except to delete the entire grid and start over.