Gray Susan,
Are you seeing the borders go away in a clean, new/empty project?
What I did to isolate my issue to the SmartShape was to start with a clean project and then insert or import the assets that I thought were the likely culprits one at a time, doing a quick F12 preview after each was added to see which asset caused the problem. Might be worth a shot.
Originally, based on the 'resize it in Photoshop and update' suggestion from another user, I had a hunch it might be image formats - like one my images was a bmp or png or whatever that was causing it. But for me it turned out to be the SmartShape. Do you have any swf files inserted? Those would be vector, like the SmartShape. Something to try. Grasping at straws Image may be NSFW.
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