Unlike other pages in Groups, home pages are currently lacking direct access to their edit screen. That is, they don't have the Edit Content tab at the top when viewing them.
In order to edit them:
- Go to the Content section of the group to view all the pages available in the group and
- Look for the home page, this may have the group name or may be called "landing" or "home" page.
- Once identified use the "Operations" menu button to select the Edit node option.