For the editor to appear correct for yourself, you must convince your browser to clear it's cache for the icons.png image. Go to htt://yoursite.com/path/to/ckeditor/skins/moono/icons.png and then use Ctrl+F5 or Cmd+Shift+R (mac users) to tell your browser to not use the cache and fetch a new one, which will then be stored in the cache.
HOWEVER, you cannot expect your website users to do this. If the image is cached on their machines as well, then they will still be seeing the problem. The only way to fix this is to change the URL of the image, which will require replacing the new url in the CSS file (it's the background image for all the buttons).