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On our blog, when a post doesn't have any images, Facebook picks banners from the sidebar for the thumbnail images.
Is there any way to let Facebook know that those images should not be used?
It's not exactly what you've wanted but you can try that way.
You can put a meta code for facebook image, your logo for example. put this in your code and every time you will have your logo as an option.
<meta property="og:image" content="http://example.com/logo.jpg"/>
Required, but never shown