MTA is "mail transfer agent", the universal standard at one time was Sendmail (on 'Nix), but many others are now as or even perhaps more popular.
If your site is being hosted on Windoze, I have no idea which MTA they might be using. Exchange Server is one.
My ISP uses SMTPD on Win2K, which was for a long time a notorious spam magnet, and some spam catchers will still reject mail off of it, particularly if it has lots of punctuation in the subject line, for example.
I'm not at all SURE that this is the problem, but it very easily could be. I'd ask cautiously whether or not they changed their server's mail programs on/about the date you first noticed the activity.
dalecosp