This green banner featuring the Snoopy character from the Charles M. Schultz cartoon "Peanuts" is a souvenir of the Apollo 11 mission. Schultz allowed NASA to use the copyrighted character of Snoopy from his popular newspaper cartoon strip "Peanuts" as a part of NASA's internal promotional campaigns to promote workplace safety, product quality, and focus on the overall mission. Snoopy's frequent depiction as a pilot (notice his World War I flying ace scarf around his neck below his space helmet) lent itself to the character's depiction as an astronaut. This banner, which was a part of a larger collection of Apollo 11 memorabilia that became a part of the National Collection in 1985, mostly likely originated as a part of NASA's flight safety efforts and celebration around Apollo 11.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.