are you talking about the list of unread posts that appears for users at the bottom of the group view page (main forum page)?
if so, its done by template function… as is most display items… you can completely customize the display.. so you can add, remove or change display items… in this case you would just remove the template function that displays it.. in your sp theme, template file spGroupViewphp…. at the bottom, remove:
sp_RecentPostList(‘show=10’, __sp(‘Unread and recently updated topics’));
as always, we strongly recommend you have your own sp theme for customizations and not edit ours or you will lose changes on updates to that theme…