Having used Ubuntu since 12.10 > 14.04 LTS I prefer a transparent greeter vs the default UM greeter. I posted both here and Ubuntu Forum and found a solution on Ubuntu Forum Here are the steps that worked for me:
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re-install unity-greeter [computer had Ubuntu 16 installed with Mate desktop]
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mkdir /etc/lightdm/lightdm.conf.d
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create file 99_myconfig.conf containing
[Seat:*]
greeter-session=unity-greeter
sudo must be used to insure proper ownership
Upon reboot I was able to choose either Mate or Ubuntu and the greeter box was transparent.
I will try this on my laptop which has only Ubuntu Mate 16
Regards,
Pete