Deleting Points and routes is done from the Main Grids (Waypoint, Route, or Trackpoint). In order to delete the points (or route header), you must first select the items, then click the "Delete Items" button on the toolbar or Edit/Delete Items from the drop down menu. Press ok to confirm your selection.

 

Note that if you have multiple routes, and delete a route header row, the remaining points will be added to the route above it, and renumbered consecutively. Be sure to check for the possibility of duplicate names (Ident column) in the resulting route.