I've changed the background of my login screen using Control Centre > Login Window and this has changed without any difficulty.
However, I also want to change the lock screen background to match the login wallpaper. Currently it is set to be the same as my desktop wallpaper and I can't seem to be able to amend this, using multiple searches. If I change my desktop wallpaper then the lock screen background changes to match it. Also, the password dialog box is more in the style of lightdm-gtk-greeter and not lightdm-slick-greeter, which I am using.
I did find one page (YouTube video) that spoke about overriding the glib-2.0 schema for Mate 16.04. This didn't work for me, unfortunately.
Also the file /usr/share/backgrounds/ubuntu-mate-common/Ubuntu-Mate-Cold.jpg (also frequently suggested that this is just re-named) doesn't exist in this distro. The background for the lock screen dialog is not unique and currently matches the desktop background. Is there a way to decouple this, so that the lock screen background can be defined separately?