I added this under Children:
:-- Privacy <ref>* Privacy Level on WikiTree: If descendants want a greater privacy level, please contact the Profile Manager. All requests out-right honored. </ref>
I guess that invitation should do it. Currently set to 'green,' but "should be set to private" doesn't tell me which 'private.' And, until I did this one profile, I didn't know that I don't know.
Thank you so much for your answers. B.