I've never tried to figure out if there's a way to change anything in the welcome or share emails. If there is a way, it would probably be via the Language Editor, and doubtful you could remove these elements.
The site is actually private because it is under construction.
What I have actually decided to do is something different which will work for us.
If you look at Jen's groups pages you will notice she has forced the Members Box to go…"