post a pic

ken

The suckers should be removed. Tear them off as close to the root as you can. Tearing rather than cutting reduces the chance of regrowth, but you may have to repeat the process in the future. The pagoda dogwood, especially if it is one of the variegated types, may have been grafted or budded onto another type of dogwood understock. This can make suckering more likely, but it takes just seconds to remove any growth coming from the roots.

Just be careful-akamaine is right in saying that "tearing" the suckers off does indeed help to prevent immediate resprouting. But since we can't see your plant, it is at least possible that these suckers are already too stout to be handled so. In that case, just take your lopping shears and cut at ground level. You may have to repeat, but really, is it that bad?

+oM

Here is a picture of the suckers. Sorry it took so long, but I'm not very tech-savvy. There are two, and the larger one is about the size of my thumb. Is tearing still a good option? (Oops! As I said, not too tech-savvy. lol)

Hard to be sure even with the photo, but try carefully scraping away some of the soil above the suckers on the side away from the trunk. If you can see where the suckers are attached to the root, great. Even if you can't, try tearing them off by sharply bending them away from the trunk. If they won't come free, then use pruners or loppers, then put the soil back over the roots.