Lunaria annua, money plant, is a biennial that looks to my eyes like a woodland plant native to America. Lunaria, however, is most definitely not native, having been introduced from Asia. Whether it can be considered invasive or not is a matter of some minor debate.

Is it possible for a plant to be considered mildly invasive I wonder? Oregon and Washington definitely are keeping a wary eye on Lunaria annua.
There is no consensus about the true threat of money plant to native ecosystems.
It is a pity, because Lunaria is a charming plant, with gentle purple flowers above sturdy stems in the woodland landscape.
Lunaria is naturalized so it is most likely here to stay. Watching its growth habit, money plant does not seem to be geared towards mass coverage of space, choking out all in its wake. If there is such a thing as a civilized invasive, perhaps it is Lunaria annua. Maybe decades from now people will even accept Lunaria as a welcome immigrant. Or maybe they will read these words and think me naive.
Lunaria means ‘moon-shaped’ and is so-named due to the shape of the seed pods. The seed pods have also led to one of its many common names: money plant. There are many more: Chinese money, silver dollars, pope’s money, coins of Judas, and a little ironic considering the preceding names listed: honesty plant.
In true biennial fashion, Lunaria annua does not bloom the first year. Reports are it will grow anywhere, including full sun. One thing that is consistent for gardeners everywhere is that Lunaria annua is easy to grow. Hardy USDA zones 5-9.

Is there a good way to distinguish Money Plant from Garlic Mustard? Hairy stems? Smell? In your last photo, the leaf closest to the bottom of the frame has a heart shape in which one of the lobes overlaps the other. Is that a key to identifying Money Plant?
smell and taste the difference. One tastes like garlic and mustard and has white flowers. Lunar has purple flowers and forms seed pods quickly after blooming