Oh, yeah, just remembered the other thing I was going to say:
Just taking a wild guess, I checked Mailman version. The host is running Mailman 2.1.29. If possible, this should be upgraded to 2.1.39 as a priority task, IMO.
Additional really good reason: Recent versions of Mailman allow enabling an effective mitigation method, per-list, for sending domains with strongly asserted DMARC policies. Currently, we cannot do that.