Jennifer, you might be able to move a bit of dirt away from the area the new growth is coming from to see if it's coming out of the tree peony stem just below ground level or if it's from the nurse roots. You're right, the color is the same as your tree peony. I do see why graycrna4u thinks it's herbaceous, though. The pictures do look like it's further away from the limb that feels right for tree growth. I see the exact same thing right now though on a Phoenix White in my back yard--new growth is coming up beside the tree rather than from the stem. I KNOW that it's tree growth though because it's been in that same spot now for 5 years and I know what the new growth looks like.
He's right--if it is herbaceous you need to pinch it out as soon as possible. I'd just do a bit of very cautious digging to confirm either way.
