I think there's now an option for this in:
- Ubuntu MATE panel layout: Brisk Menu -> search for Screensaver.
- Traditional panel layout: System menu -> Preferences -> Look and Feel -> Screensaver.
In the dialog that pops up, go to the bottom of the dialog and there should be an option for the wallpaper shown when the screen locker displays the password prompt. Choose appropriate wallpaper.
(This feature is new to MATE 1.24.)