When the light enters the first lens, it flips the image upside down. The second lens sends the light straight into the 3rd lens. The 3rd lens focuses the light into a point about 3 inches past the lens. Since the light is focused into a point, any object placed around that point cannot be seen when looking through the lenses. The light is essentially bending around the object. Once the light hits the point just past the 3rd lens, it then flips back right side up. This allows the background image to pass through all of the lenses without warping or being seen as upside down.
This project was inspired by the Rochester Cloak experiment created by Professor John Howell and graduate student Joseph Choi. Be sure to visit their page to learn more about the experiment:
http://www.rochester.edu/newscenter/watch-rochester-cloak-uses-ordinary-lenses-to-hide-objects-across-continuous-range-of-angles-70592/