Facebook grabbing wrong photo

I have had 2 clients that have had a similiar issue, and am wondering if there is a way to make sure facebook does not grab an image. They are both using an auto-post method for Facebook.

Both have a free offer graphic on the sidebar, and rather then grabing the picture within the post it grabs the free offer graphic.

Is there a way to say NEVER use this graphic for facebook? Or is there a better way to go about this?