Title of email was "We can't migrate your WebFaction website." Which made me breathe a sigh of relief, and I almost did not bother with reading any further. But I did read on, and found the reason given as "Custom app (listening on port)."
What they could have done was say something like this:
"We would like to try to migrate your website. We notice that you have a Custom app (listening on port). Did you know what you were doing when you created this app (more than 5 years ago), and do you still need it?"
If they had asked those questions, my answers would have been "Only minimally" and "No".