I would just leave them. They are a spring wildflower and will die back just like the Trilliums.

Here is a link that might be useful: Trout lilies

I also vote for keep! They are spring ephemerals and will die back before anything you plant in the area starts growing for the season. They are also rather sensitive to disturbances in my experience, and may just stop growing in areas you garden in on their own.

How I wish I had your problem. I love trout lilies, and had a few at my old lake house. I covered the holes left in the flower bed with hosta, but I'm sure there are many other later blooming flowers that would work as well.

Definitely keepers, both kinds. Beautiful Wisconsin wildflower and should be left to grow.
We have so many invasive species, and it's refreshing to hear of a healthy population of Trout Lilies in someone's garden.