/usr/share/gdm/greeter/ is in gdm3 3.18.3-0ubuntu2.
This file is owned by root:root, with mode 0o755.
..
/usr/share/gdm/greeter/applications/
/usr/share/gdm/greeter/applications/gnome-shell-wayland.desktop
/usr/share/gdm/greeter/applications/gnome-shell.desktop
/usr/share/gdm/greeter/applications/mime-dummy-handler.desktop
/usr/share/gdm/greeter/applications/mimeapps.list
/usr/share/gdm/greeter/autostart/
/usr/share/gdm/greeter/autostart/orca-autostart.desktop
/usr/share/gdm/greeter/dbus-1/
/usr/share/gdm/greeter/dbus-1/services/
/usr/share/gdm/greeter/dbus-1/services/org.freedesktop.Telepathy.AccountManager.service
/usr/share/gdm/greeter/dbus-1/services/org.freedesktop.Telepathy.MissionControl5.service
/usr/share/gdm/greeter/dbus-1/services/org.gnome.OnlineAccounts.service