The Complete button should be hidden from the user because of the following:
  1. Custom Kanban bars are the most important indicators regarding status of an item. So the in-built status of New/InProgress/Completed should be assigned to an item automatically and every time just after user drags an item from one Kanban bar to another. There is no need to involve user to do that manually. The most annoying situation is when I drag an item from the Kanban bar Done to some previous bar and see that in-built status Completed remains.
  2. Removing the most unnecessary button Completed will lightweight an UI of item which is quite overcrowded with other buttons and icons.