Hi Joannakat. Itohs do put out pips on the lower stems like their woody peony ancestors but in the colder zones those typically don't survive the winter; I've never had growth from them in my zone 4b garden. They also form eyes below ground so the loss of the stem pips isn't significant. I've heard that in the warmer zones those above ground pips put out growth before the below ground eyes, assume they eventually even out in growth but it'd be super cool if having growth from both extended the bloom period....
If you want to try to keep the above ground pips I'd mulch them through the harshest winter months and remove it as early as possible in the spring. Keep an eye on it though because mulch can create a nice mouse hotel—it'd be awful to do something to try to keep those pips and have more of the plant destroyed by pests....
