When I entered sudo apt remove ubuntu-mate-default-settings
in the terminal I received the following output:
steven@Inspiron-3542:~$ sudo apt remove ubuntu-mate-default-settings
Reading package lists... Done
Building dependency tree
Reading state information... Done
The following packages will be REMOVED:
mate-desktop-environment-core mate-gnome-main-menu-applet mate-screensaver
mate-session-manager ubuntu-mate-core ubuntu-mate-default-settings
ubuntu-mate-desktop
0 upgraded, 0 newly installed, 7 to remove and 0 not upgraded.
After this operation, 3,686 kB disk space will be freed.
Do you want to continue? [Y/n]
This tell me that if you removed ubuntu-mate-default-settings you also removed the mate desktop as well. See mate-desktop-environment-core, mate-session-manager, ubuntu-mate-core, ubuntu-mate-desktop in the terminal output.
You could try reinstalling these packages and see what you get
sudo apt install mate-desktop-environment-core mate-gnome-main-menu-applet mate-screensaver mate-session-manager ubuntu-mate-core ubuntu-mate-desktop
Otherwise it might be time to backup any files you wish to keep and reinstall.
Edit:
If your left with a desktop that you can no longer log into, you can boot your machine from a live session and transfer any files you wish to keep to a external drive, prior to reinstalling Ubuntu Mate.