Hi and welcome to the Ubuntu MATE community,
It's a bit tricky as there has not been yet an utility to customize the new Arctica Greeter. There's been several threads about this.
Here's a comment explaining how:
Basically, you need to edit a file with the path to your desired background and then run another command.
To do so, in a terminal, enter:
sudo pluma /usr/share/glib-2.0/schemas/30_ubuntu-mate.gschema.override
and edit line 2 (background='/usr/share/backgrounds/ubuntu-mate-common/Green-Wall-Logo.png') , replacing the path with the one to your wallpaper and save the changes. Don't screw up or it could cause trouble.
Then in a terminal:
sudo glib-compile-schemas /usr/share/glib-2.0/schemas/
And that's it.
Hope this helps.