In Admin > Site Settings > Advanced Settings > Usability Settings, you can set control panel view mode to view or edit. Setting it to view will remove it to page editors

if you see the bar when you are not logged on that means you have edit rights on the page or on a module. It would be advisible to review permissions on the page as well

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I had the same promble.  The mode edit/view was showing when logged out on 1 page of my web site.  All of the pages had page editor view & edit rights.  I removed the page editor rights from the page where the mode was showing and logged out - it was gone.  i put page editor back on, logged back out and mode was showing on the page again.  I created a new page, exported the content from the page that was having the mode problem, imported it to the new page, set page editor on the new pagfe, logged back out and the problem is gone.  I deleted the old page that was having the problem.  Why did this happen and will it come back?

DNN 4.8.3