A resident who has been banned from a parcel/region should not be able to message other residents on that very parcel/region. (Exceptions could be, that they are on their friend list or have been contacted before yet.)
Reason: This could help to prevent more drama and protect businesses. A griefer who is banned from our shipyard is frequently camping next to it and messaging our customers defaming us trying to deter them from buying our ships. I'm sure we are not the only ones who have this problem.
Edit: Additionally I would suggest that a banned resident should not be able to see other residents on the land he is banned from, neither inworld nor on the minimap. (Thank you @Bavid Dailey for this idea!) I think, this would make the "work" of any griefer harder, too.