So...the TM is just an attempt to appear legitimate and carries no weight at all except for appearance.
A TM can be defended in a court of law for trademark violation litigation, but only if the trademark holder can prove somehow that they have been using it historically earlier than the other party.
In the society's case, publications with a certain copyright date would suffice as evidence of historical use of a trademark.
Obtaining a ® means that any litigation defending the trademark would be much swifter. Evidence needing to be provided would only be the registration documents and nothing more.
Also, remember that a TM is still copyrighted by the original creator of the artwork. So, in this case, the JW dot ORG logo is being used as an unregistered trademark by the society, and it's also subject to copyright laws for reproduction of the logo.