Alexander Pensky expounded:

So, all you tree peony owners out there, what do you think? Do tree
peonies normally put out an explosion of topgrowth in mid-spring just
after flowering, and is it normally a little bit "coarser" than the
older leaves? Or do I have a sucker coming from the rootstock which
should be removed?

Dig gently around where the leaf stalk comes up and see where it
originates. It certainly sounds like a root shoot and that it should
be clipped, but be sure before you use the pruners.

--
Ann, Gardening in zone 6a
Just south of Boston, MA
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