This topic is one for Help For Tamagotchi Owners, not Stuff We Read, so I've moved it over there.
You haven't specified which Tamagotchi version you're using, but I do know what you're referring to. What you're seeing is a decoration for Hinamatsuri, also known as Girls' Day, which is a Japanese festival which takes place on March 3rd. The "weird couple picture thing" is a display of emperor and empress dolls, and is a simplified version of a traditional Hinamatsuri doll display.
A traditional display tends to look a bit like this. It features the emperor, empress, and their royal court, all decked out in Heian-period dress.
I think that the dolls here look considerably more goofy than the ones in real-life, I must admit, but it's fun seeing it get a nod here. I was first introduced to Hinamatsuri by its appearance in an episode of the Pokemon anime back in the late 1990s, myself.