Tree Peony Suckers

Just a few weeks ago, I was rejoicing that the herbaceous peonies (Paeonia lactiflora) were emerging and I remarked on Facebook that they resembled hands reaching to the sky.

But when I saw this at the base of my tree peony, I wasn't happy at all:

Tree peonies (Paeonia suffruticosa) are generally grafted onto a P. lactiflora root and occasionally they'll try to grow from below the graft.  Since you probably paid good money for that tree peony, you don't want something sapping the strength from it and that's just what the herbaceous peony shoots will do.  Besides which, they'll bloom like an herbaceous peony, too.

So, what's a good peony mother to do?

Nip it.  Nip it in the bud.  Carefully cut the suckers off at the ground and keep them cut.  Later, in the fall, you can dig around the roots and see if the tree peony portion has formed its own roots.  If so, you can trim away the herbaceous roots to prevent suckering in the future. (Instructions for this can be found at peonies.org.)

I'm not sure that's entirely necessary though.  I feel more secure in just keeping the suckers trimmed away.  Can someone smarter than I am about these things comment here and let me know if this is an acceptable way of dealing with this issue, or whether I will eventually need to deal with the herbaceous roots in a more permanent fashion?

Tree peony (unknown cultivar)