I can’t remember which version transition of Access heralded the change from open-tables-as-floating-windows to the more strict left pane list, and right pane workspace. I’m not even sure I ever used Access 2003 - I cut my teeth on 97, dabbled with 2000, and hardly touched it again until 2013.
Access 2016 doesn’t allow you to delete a table from the list in the left pane if the table is open either in the ‘table view’ mode (where it looks like a spreadsheet) or ‘design view’ mode (where you can set the field properties) - 2016 pops up a message box specifically saying that you must close the table before you can delete it. I am not sure what 2003 does, but it wouldn’t surprise me if it just greys out the delete command.
If you have no tables open as tabs in the right hand workspace, and you still can’t delete tables in the left pane, then the problem must be something else (and I am not sure what that might be)
I’m not sure what you mean about never opening tables - in your other threads, you discussed the columns being in the wrong order, etc - how would you see that without opening the table?