I’ve been struggling with this myself over the last few months, so I looked over every single option, to see if I could find anything to fix it, and I may have found it.
In the Excel options, there is a section at the very end called “Trust Center”, and there I clicked on “Trust Center Settings...”.
Under that there is a section called “Message Bar”, which I believe is the name given to the line that displays the backup warning message (and others).
After selecting that section, I noticed there is a subsection called “Policy Tips”, so I disabled the option ...“Show Policy Tip in the Message Bar. Turning this off will disable all Policy Tips unless your organization requires it."
For now, it seems to have worked, but I will have to wait longer to confirm.
EDIT: To test it, I cleared the "KFMLastDismissTimestamp" registry entry, and the annoying nag message came back.
So, the above does not help!
I found a similar setting in Word's "Trust Center". Running the same test to see if this is better than the KFM... patch, got the same disappointing result.