Is this Nandina?
Yes this looks like nandina domestica, heavenly bamboo. In Maryland, Nandina domestica has been classified as a Tier 2 Invasive Plant, and now requires a warning label for potential environmental harm where it is sold. We do not recommend planting it.
However, you do not have to dig up the plants. Have a plan to replace them if they decline or you need to redesign your garden. When you replace use native plants that produce berries for wildlife.
If the plants produce berries, prune and dispose of so the birds do not eat them or
spread them. Some cultivars do not produce berries.
You may want to look at the publication from Clemson on nandina. See the information regarding toxicity and birds. http://www.clemson.edu/extension/hgic/plants/pdf/hgic1071.pdf
Here is a link from the Md Invasive Species Council, Invader of the Month for 2/18. http://mdinvasives.org/iotm/feb-2018/