This only happens with one specific spreadsheet.

In the file structure I delete all documents named "Backup of X". Then I
edit spreadsheet "X". Upon closure of the Excel session, I see in the file
structure again, "Backup of X" with the time and date stamp of the previous
session.

I have looked In Excel Tools - Options - General tab - Default file location
and Excel Tools - Options - General tab - Save tab - Autorecovery file
location. Neither are pointed to a network environment where this is
happening.

I suspect it is a either a Macro or Visual Basic script executing on this
one spreadsheet. I have looked at the Macros and Visual Basic scripts I can
see and I don't see anything I would consider suspect.

Does anyone here know?