To remove a particular Wall story:
- Hover your mouse over the right corner of the Wall story
- Click the "Remove" button
- Go to the Application Settings page from the Account drop down menu.
- Click the "Edit Settings" link next to the application you would like to edit.
- Select the Additional Permissions tab in the box that appears and uncheck the box next to "Publish recent activity to my Wall."
- Click the "Okay" button.