Calm down, it’s OK, they’re suppose to be there. They are eating away at the sweet coating that encases them.
Some say you can blow them off, some say you must leave them alone or the flowers won’t bloom. I say why take the chance, they’ve been crawling on theses flower buds since time began; I don’t think Noah was blowing them off way back then, and here we are 2017 and we’ve still got Peony’s coming up.
But, in a few days from now you’re going to see these in bloom all over the place; you are going to smell them as you walk by, you are going to chat with the procurer of these beautiful flowers, and you’re going to want one or two of them in your yard. And this is where a little knowledge is going to come in handy, for chances are the well meaning Peony grower is going to offer you a division of theirs; he might even run and get his shovel and stomp out a little clump for you on the spot; and this is fine, it will transport in your hand with no problem. But planting it is where it can get a little tricky.
If you plant it to deep energy is spent struggling to the surface and therefore no flowers. To shallow of a planting and it has no support and keels over. You must plant it exactly as it was in the ground before it was dug up. So run back, hopeful Mr. chatty Peony person is in the house, look at what is exposed in the original bed, and run back a plant yours accordingly. And latter on don’t freak out over the ants.