Basj,
I performed the "purge and reinstall" as requested, but the results were the same. However, I also found a GroupyOnOff.bat file that allowed me to quickly test different scenarios. So I have a lot more information for you now. 
This is what I have found from my testing...
- I have a multi-monitor setup (4 monitors)
- The Groupy tray icon is NOT there on bootup (good/normal)
- If I group windows on my 'main' monitor all is well (good/normal)
- If I group a window on my 2nd, 3rd, or 4th monitor while the window is NOT maximized fullscreen then all is well (good/normal)
- If I group a window on my 2nd, 3rd, or 4th monitor onto a window that IS maximized then the issue occurs (bad)
Interesting also is that I do not even have to group the windows for the tray icon to appear. As soon as I hover my 'dragged window' over to the window to group with (again, this window is maximized, fullscreen, on a non-main monitor) and as soon as the text "Group this window and the dragged window" appears so does the tray icon. I can then move the window away and 'not' perform the grouping, but the icon still remains. The only way to have the tray icon go away is to run the GroupyOnOff.bat file, or reboot.
Finally, to recap. The issue does not occur on my main monitor, whether the applications are maximized on that monitor or not. The issue only happens on any one of my non-main monitors and only if the window I am dragging a window onto is maximized full-screen.
I hope this detail helps and you are able to reproduce the issue. Let me know.
Cheers,
Russell