Gmail app on iphone shows notifications for 'everything' instead of just inbox
Went to updates.  Loaded the latest update for the gmail app (Escaped -- er released -- 18 September)

Problem vanished. 

Edit 2 days later: 

Or seemed to.  It's back now.  I've reported this bug now both from the Gmail App and from the desktop app.  We will see if Google takes action.  While I'm waiting I'm looking for other apps tha understand gmail labels.