...if you're using a masking technique to create the material on the inside of the lid I don't see why my last suggestion still wouldn't be a quick, viable fix. Make the area transparent and put a one sided square in its place, very slightly intersecting the sides? It would be an incredibly easy thing to do in a modeler, and only slightly more tedious within Poser. Would probably only be noticeable in very extreme close ups, and maybe not even then.