Unfortunately, if you are placing the Recent Activity Widget on the home page, there is no context...so it pulls from the System Context. Your best option is to either remove the widget and/or generate more activity in other areas to drown out the undesired activity. (I'm pretty sure that isn't a configuration in the widget, but I'd double check). Besides that I would possibly ask around to users to get the consensus of the impact of seeing that information on the home page. In general, once Jive gets up and running, these type of updates do get drowned out.
Hope that helps.