How can I disable/modify the SSH login banner for a given user?

It seems it is possible to disable this message on a user basis by creating an empty file in a user's $HOME directory (/home/username/) called .hushlogin.

touch ~/.hushlogin

If you want to disable that message for all ssh users, edit /etc/pam.d/sshd and comment out the lines

session    optional     pam_motd.so  motd=/run/motd.dynamic noupdate
session    optional     pam_motd.so # [1]

In /etc/ssh/sshd_config make sure there is a line:

PrintMotd no

If it is set to 'yes' change it to 'no'.

Restart the SSH server by typing

service ssh restart

You should be good to go from there.