The souvenirs that the parent takes with them, when they leave, depend on the Tamagotchi Connection version.
For V3, s/he takes the two keys from the Town Hall, the medal from the School, the cell phone from the Parent, the BMX bike from the GrandParent, and all of the items s/he won in the Arcade games: skateboard, balloon, baseball cap, and teddy bear.
For V4 & V4.5, s/he takes all souvenirs except the travel souvenirs, the gifts from the king, and the movie posters.