Peonies produce nectar on the outside of buds which attracts ants looking for an early season food source. There is a myth that ants are necessary to get the buds to open. Blooms are not dependent upon ants, rather ants depend on the blooms for sustenance.
Ants are not problematic for the blooms and insecticide is absolutely NOT warranted. In fact, some sources state ants help deter pests that would cause harm to the blooms. As the blooms reach their peak, ants typically move to their next food source.
Gardeners who intend to harvest peony flowers for the home, should cut before the bloom is fully opened, preferably early in the morning. Buds will continue to open once placed in a vase of water. If ants are present when harvesting, hold the stem, upside-down, close to the bloom and gently shake to dislodge ants. The blooms can also be lightly washed to remove ants.