Every Space Shuttle crew designed its own unique mission patch featuring their names and symbols that suggested the nature of the mission. This patch design represented the STS-80 mission in late 1996. While on Columbia, the crew deployed two satellites and later retrieved them. Those payloads are depicted above and below the three curved red lines that mimic the symbol of the astronaut office -- a star rising on three rays encircled by an orbit. This is probably an extra patch like those stitched on or attached to a spacesuit with Velcro. NASA transferred this patch to the Museum in 2012.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.