Fred
while the table is in its native form, the text data is linked to the points that it is derived from so theoretically the table does know which points it contains. If you edit the table it tells you that it contains 10 points etc. and if you move a point or change a point elevation the table updates - so it does have the references required to be able to select the points to which it refers or to create an output from the table of the points to a CSV for example.
Challenge is that there is no way to do that from the UI as it stands today.
If you made a selection set of the points prior to using the selection set to create the Table you would be able to recall the selection set anytime and add to it or remove from it, so maybe just change the way that you make the selection of the points to create the table if that is the case - use the Selection Explorer, select the points and then "Create a Selection Set" and name it eg Point List. Then you can Lock the Selection Set to protect it. When you create your table and are asked to add Points, you open the Selection Explorer and double click the Selection Set you just created and that will select all the points and then you can add them to a Table.
Now that you have the Selection Set saved, you can use that to select the same points and output them to any point format or DWG/DXF that you may want.
Alan