The Distinguished Houseguests are four life-sized dolls by the fireplace at Jade's house. They like to gather for tea in a mannerly and civilized fashion. One of these houseguests is a VALIANT KNIGHT, with a suit and helmet. Another is a DECREPIT MUMMY with a Napoleon-like outfit. We could only see the silhouettes of the other two until John accidentally dropped the Typheus minion on top of them all. This revealed the remaining two to be a sun-bleached BEAUTY, and the other a stuffed BIG GAME TROPHY with antlers and a white tuxedo.
All four of these indicate Jade's grandfather's interests (hunting, knights, beautiful women and taxidermy), just as the other Homestuck kids' guardians have the same sort of doll. They were initially believed to be involved in the prototyping of Jade's Sprite, as it was is implied that Grandpa intentionally gathered a variety of choices for Jade's Kernelsprite (due to him having insight into the workings of the game beforehand). An accident left them in a pile with Grandfather's stuffed corpse and a stuffed Typheus minion, dangerously close to the Kernelsprite. John attempted to prototype the sun-bleached beauty, hoping it would make Jack Noir less powerful, but was interrupted by Vriska. Bec then warped the entire pile into space, and prototyped himself.
The "blue girl" (the sun bleached beauty) was on some strange pretend date with Grandpa at the time of his highly convoluted death. This led Jade to develop a childhood fear of the doll, believing that she might have committed the murder. She haunted Jade's dreams until Jade grew out of it.