You can configure the Facebook element on your social media mashup page so that it either displays all of the content posted to your Facebook Wall (including that posted by others), or just the content that you post to Facebook. Open your mashup page in the Unpublished tab, hover over the Facebook element, and click the yellow pencil icon to edit the settings for the Facebook element.
Note: Your site's appearance may vary, but the method of editing the Facebook element's settings will not.
There is a dropdown setting that lets you choose to display all Wall posts, or only ones from the page itself.
By selecting "Wall Feed," any content that's posted to your Facebook page - whether by you or by someone else on Facebook - will appear on your mashup page. Use the "Only posts from this page" selection to ensure that only the content you add to Facebook will be displayed on your site.