Ask Mr. Smarty Plants

This is a toughie, because I was unable to find any negative comments on Claytonia virginica (Virginia springbeauty), or ways to get rid of it. According to this USDA Plant Profile, it is native to just about all of Illinois, including Marshall County. You are in USDA Hardiness Zone 5a, which is well within the tolerance of Spring Beauty, hardy from Zones 2 to 9. We even have some growing in Travis County, where the Wildflower Center is located, but Central Texas is really not what I would call a cool, moist woodland. We found this site from Illinois Wildflowers Spring Beauty, which, again, had nothing but nice things to say about the plant, which grows from small potato-like corms. Dave's Garden, a garden forum, also had mostly positive comments on Claytonia virginica.

We really can't even recommend any sort or herbicide, because the use of it would threaten other plants around the ones you want to get rid of, but not put Spring Beauty into any particular danger because it can regrow from those corms in the ground. According to our page on this plant in our Native Plant Database: "Plant disappears from above ground shortly after the seed capsules have ripened but does not leave a large gap in the garden." Speaking from very hot and dry Texas, we would think it would be lovely to have flowers beginning to bloom in the depths of Winter, and then disappearing until next year.

In view of the way the plant propagates itself, we would recommend first that you mow the lawn pretty low while these flowers are blooming, both preventing the re-seeding and also denying the nourishment of the leaves to the corms below ground. Second, if you don't want it in your flower beds, digging out that corm, which is about 3" deep, and continuing to do so until it gives up and starves is about the best bet. 

From our Native Plant Image Gallery:

Claytonia virginica

Claytonia virginica

Claytonia virginica

Claytonia virginica