UPDATE:
NOT A LEMUR
NOT A PANTHER
NOT A GAME SHOW
BUT IT MIGHT BE A BEAR
According to Boing Boing reader Malcom Bell: "ItteQ is a travel show and this is a one-off. The woman in the box is Imoto Ayako."
Imoto Ayako
The show is called Sekai No Hate Made Itteq! (translated: Riddles at the Ends of the Earth!)