Thanks for all of the ideas. Here is an update to your questions and ideas.
The manufacturer does not provide or mention a filter, so I doubt it. But, who knows. If I can put my hands on a DSL filter, I'll give that a shot.
Unplugging the Lifeline does "fix" the Mailbug.
There is a way...
Solve this Electronics Mystery!
Hey guys - I really need some help from you experts. My elderly mother and father-in-law have two electrical devices that are, for unexplained reasons, totally incompatible with each other. I need some ideas to identify solutions for this bizarre problem...