Removing the dead blooms from your peony plant promotes leaf and flower production. Deadheading is another term for this practice, and it can keep your plant looking attractive.
Peony seed pods are interesting.
Leaving the dead blooms on your peony plant will allow the interesting-looking seed pods to appear. This might be useful if you want a more eclectic look for your garden or would like to use the plant for educational purposes with children.
Deadheading your peony might encourage growth, but leaving the dead blooms alone will not harm the plant. Gardeners should make the decision that best suits individual gardening style.