What is this button on my MacBook Pro Touch Bar? I've highlighted it in red in the screenshot.  It seems to show up almost all the time on my Mac, regardless of what applications I have open.  Pressing it does nothing apparent.  If I "Customize Control Strip..." in System Preferences, it disappears.  It does not appear on Apple's list of touch bar icons.

I'm running macOS 10.12.6 on a 13" MBP.
That looks like it is from BetterTouchTool. You can configure it in the settings for BTT:

https://github.com/fifafu/BetterTouchTool/issues/1033


  fifafu: You can disable it in the Touch Bar settings in BTT (go to the Touch Bar tab, then click the "General Touch Bar settings" button.
  This may require a restart of BTT to become effective.