How did calibre get to the tray, via the setting in Prefs->Look and feel or via a 3rd party utility, e.g. the one you use for Stay on top.
I just changed the L&F setting to minimise to the tray, restarted and minimised calibre - I didn't change the Windows setting to show on taskbar, so it was in the tray, and then did an install an got this:
My extra buttons utility has a minimise to tray feature that has given me grief. I used it once inadvertently and the task disappeared into the wilderness, had to kill it with task manager, so I have that option disabled. I limit my tray icons to tasks that are run at startup, Programs I run on demand that pop things in there irritate me - task manager, outlook etc.
BR