Hi Geogirl, the way to remove green flags from shape vertex is to select them and right clic to delete marker. However I think you cannot detach markers from vertices once that they are attached.
If you dont want markers on shapes, uncheck the option that makes them to be attached automatically to every shape while it is been drawn. Menu option Tools-markers-attach markers.
If you have already created lots of shapes and want to get rid of attached vertices, I can export shapes, delete and then import them again.
Good luck
GEOBIT