Peg, cutting a single 6" piece of feeder root off the side of a very well established peony isn't going to faze it at all. Those roots are basically food storage and I bet yours has more than enough to weather the loss! I've actually heard of growers removing pieces of feeder root to stimulate root growth....
Now depending on the variety some herbaceous peonies will practically insist on being divided. If you notice your peony putting out less buds than normal years or growing in almost a donut pattern with a bare center you'll want to dig it up and divide it once it goes dormant in the fall. I suppose if yours has been in place for 20 years now with no ill effects you probably won't see those issues! Welcome to the peony forum!
