From the Super Mario Wiki
The Mudroom Exterior (Forgotten Garden in the British English version) is an outdoor area in the Gloomy Manor accessed by exiting through one of the doors in the Mudroom in Luigi's Mansion: Dark Moon. The Mudroom Exterior is similar to the Front Yard, but smaller. There are several shrubs surrounding the area and the ground is grassy. There is a narrow tile path that leads to a more open area of the Mudroom Exterior. This larger area of the Mudroom Exterior contains two leafless trees, one of these trees has an Amethyst on one of the branches. There are also lampposts, a doghouse, and plants. A Polterpup can be seen playing with an Amethyst in the Mudroom Exterior when the area is viewed from a window in the Mudroom.