You can set a background picture for the gdm login-screen this way:
Install systemd-container
sudo apt install systemd-container
and, if you like to add a blur effect to your picture, imagemagick (or another image editing tool as e.g. gimp, but imagemagick is a command line tool which is really small compared to gimp)
sudo apt install imagemagick
To add a blur effect to your picture, e.g. run
convert path/to/input-image.jpg -blur 0x50 path/to/output-image.jpg
You can play with the values for the blur radius and sigma (e.g. 0x20 is less blur) and use different image file formats
convert ~/Downloads/image.jpg -blur 0x50 ~/Downloads/image-blur.jpg
If you like, you can additionally darken your image with imagemagick. Then use this command instead. Play with the values for the brightness and blur. When you set higher negative values for the brightness as e.g. -20, -30, -40, .., the image gets darker.
convert ~/Downloads/image.jpg -blur 0x50 -brightness-contrast -10 ~/Downloads/image-blur.jpg
Then copy the edited image to /usr/share/backgrounds because gdm can't reed the images in your home directory:
sudo cp path/to/output-image.jpg /usr/share/backgrounds
e.g.
sudo cp ~/Downloads/image-blur.jpg /usr/share/backgrounds
If you don't like to add a blur effect, just copy your original image to /usr/share/backgrounds.
Now start the systemd-container to login as gdm user:
machinectl shell gdm@ /bin/bash
You are prompted for your password.
In the terminal you see that you are logged in as gdm user now, when it shows gdm@zorin:~$
Then set your image as background wallpaper for gdm (enter the path of your image at /usr/share/backgrounds here), e.g.:
dbus-launch gsettings set com.ubuntu.login-screen background-picture-uri 'file:///usr/share/backgrounds/image-blur.jpg'
dbus-launch gsettings set com.ubuntu.login-screen background-size 'cover'
Then exit the container
exit
and logout.
To undo it and go back to Zorin's default gdm login background screen, run
machinectl shell gdm@ /bin/bash
dbus-launch dconf reset -f /
exit
You can remove the installed packages with
sudo apt purge systemd-container imagemagick
Then logout.
This method is an alternative to the app gdm-settings or scripts if you just want to set a background image for gdm.
It is possible to make some other settings for gdm this way as shown in Arch wiki, but not all worked in my test. With the dconf reset command above, you can undo all settings you made for gdm in the container.
The app gdm-settings is easier to use, but I tried to show an alternative. So far, there haven't been any instructions on this method in the Zorin forum.