You can update and/or add new objects to the other application by selecting them and clicking the Update button or selecting Update Current Scene. Objects are not deleted using the Update functionality. If you no longer want to use an object in the scene, you must delete it.
Selecting Update Current Scene adds non-existing scene objects, while selecting Add to Current Scene duplicates existing objects instead of updating them.
For update operations, the control rig, skeleton, and bound geometry are considered separate character elements and are handled independently. See Selecting character data to update current scene.
Your Maya scene is now updated with the changes you made in MotionBuilder.