You can download the GDM background changer script using wget from a terminal:

wget https://github.com/PRATAP-KUMAR/ubuntu-gdm-set-background/archive/main.tar.gz

If you only want to change the login screen colour, or apply a favourite gradient, the included README file runs through those options.

Since I know the path to my background wallpaper it’s just a case of switching back to the terminal and using cd to enter the downloaded script directory in a terminal. Then I run the script (with sudo, eek) passing it the path to the image I want to use as a background

cd ~/main/ubuntu-gdm-set-background-main

sudo ./ubuntu-gdm-set-background --image ~/Downloads/mywallpaper.jpg