Hi, 

Assuming you have this variety, Polygonatum odoratum variegatum which is quite common as it was the perennial plant of the year in 2013, unfortunately it is not native but also not considered invasive at this time. Whether you should stop giving away plants is a personal choice. In the gardening world, this is always welcome, however when it comes to the plants - if they are invasive that could be a concern.  In this instance though, what could be more so of a concern is any soil contamination with pathogens, jumping worms eggs, nematodes, or other unwanted pests or diseases . You can wash off the soil of the roots and keep them moist for planting soon after if you'd like to share. This same professor from Washington State University also wrote an article for Fine Gardening if its easier to read. 

Happy Gardening! 

Emily