Udacity - Hand under notes video effect
Most likely, they are simply using an output of the notes with transparency.  If you output the digital version of the notes with a transparent background you could just layer it over the video once properly aligned and it would work fine.  

Alternately, a quicker process if they do not support alpha is to just apply a blend between the layers.  Since the background matches the video except for where the hand is, it would blend very smoothly.

Finally, what is known as a luma-key could also be used on the screen capture file to generate transparency anywhere that the luminosity (brightness) differs from the empty background.

Any of these options could be used and they are all extremely easy to use, though the first requires the most advanced technique to generate the alpha content, but would also produce the best results.