/usr/share/gdm/ is in gdm3 3.14.1-7.
This file is owned by root:root, with mode 0o755.
..
/usr/share/gdm/gdb-cmd
/usr/share/gdm/greeter.dconf-defaults
/usr/share/gdm/gdm.schemas
/usr/share/gdm/locale.alias
/usr/share/gdm/greeter.dconf-defaults.md5sum
/usr/share/gdm/generate-config
/usr/share/gdm/BuiltInSessions/
/usr/share/gdm/BuiltInSessions/default.desktop
/usr/share/gdm/dconf/
/usr/share/gdm/dconf/00-upstream-settings
/usr/share/gdm/dconf/locks/
/usr/share/gdm/dconf/locks/00-upstream-settings-locks
/usr/share/gdm/greeter/
/usr/share/gdm/greeter/dbus-1/
/usr/share/gdm/greeter/dbus-1/services/
/usr/share/gdm/greeter/dbus-1/services/org.gnome.OnlineAccounts.service
/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/applications/
/usr/share/gdm/greeter/applications/mimeapps.list
/usr/share/gdm/greeter/applications/mime-dummy-handler.desktop
/usr/share/gdm/greeter/applications/gnome-shell.desktop
/usr/share/gdm/greeter/autostart/
/usr/share/gdm/greeter/autostart/caribou-autostart.desktop
/usr/share/gdm/greeter/autostart/orca-autostart.desktop
/usr/share/gdm/dconf/90-debian-settings