Yes. Under Settings if you click Hide/Show Other Organizations under Select Needs to Display on Your Website, if you set the Default Need Visibility to Not Visible then new organizations registering with Meet The Need will automatically be set to Hidden on this page and their needs will not appear when you show all local needs.
If you have set the Default Need Visibility to Visible but wish to prevent the needs of certain organizations from appearing on your web site, we recommend occasionally reviewing the list of organizations who have joined Meet The Need in your area in the past 5 days, past 15 days, etc. using the Joined any Time drop down on this page.