steve lund writes:
BTW, so what is this "Registering" an email server with an ISP domain?
What it says. Other than putting your domain and IP on a list, I know of no policy that's common to most such programs. :-(
Is it worthwhile trying to get our web host to do this
In general, yes. Some ISPs have provided services such as reports on issues related to your domain or IP as a sender, and while history suggests that they think that their users get a lot madder about one spam message than they do about one undelivered mail, users do care about lost mail. I'm sure they genuinely intend these programs to help your mail get through to subscribers at their services. (I don't know if any currently offer such services to registered domains.)
The ones that are reasonably good at this are providers like Gmail, Yahoo!, and O365, whose business model (at least at one time) involved provision of excellent email hosting.
There is some administrative effort required, so you could check what domains your subscribers are using and see if they have registration programs, what information they want, and what benefits they offer when you approach your host. This is the kind of thing that experienced mail hosting services do for you; you may find that they already do this "in general", and haven't registered with ATT only because ATT doesn't have a program. :-(
Steve