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?
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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"/>