When turning a round tenon on a lathe it is easy to under-size the outside diameter of the tenon. Rather than scrapping the tenon try this. Using a hand plane, shave off a length of the same species of wood from a scrap board. Coat both the scrap and tenon with glue and wrap it around the under-sized tenon and secure it with a rubber band. After the glue dries you can sand or turn the tenon to the correct size on the lathe.
Note: This technique can also be used for old chairs where the tenons have loosened over time.