Most likely these are coming from the herbaceous nurse root that tree peony was grafted onto. How deep did she plant the tree peony? One should plant that nurse root a good 8 to 10 inches deep so that the tree peony will begin to make it's own roots and the nurse root will die off. Keep cutting off the volunteers from the nurse root and this fall I'd probably dig the tree peony and plant it much deeper.
Alana, what do you think????
