Welcome. If you get the spam via inter user messages, then yes, try to remove the perm from Anonymous group.
It worked. I really appreciate your help Luci, tks.
While I'm at it, I have another question:
In the same permission page, there is a message systems function: /tiki_p_messages
(see attachement for my screen capture)
do you think it will help to slow down the number of spambots I get?