Some clarifications:
- Greeter is usual GTK3 application.
- No WM or compositor run in greeter session.
- Greeter creates one GtkWindow for each monitor.
- Greeter uses standard cairo functions to draw monitor's window background.

There are no "login" or "panel" windows - just child widgets inside fullscreen
window.
This grey color looks like default window color - just set
"background=#default" to see it.
So, the question - why gtk draw semi-transparent panel correctly (using parent
window background as base) and do not do it for "free" space.

Add "allow-debugging=true" option to lightdm-gtk-greeter.conf to get more
informative log.

Some questions:
1. What happened if background is color (#0f0)? I don't expect that there will
be any difference, just interesting.
2. Another gtk theme? Or empty "theme-name=".

I saw very similar bug some time ago - laptop with archlinux and catalyst. In
some cases gtk didn't draw whole windows except some widgets (text entries -
blinking cursor). But this bug is gone now.