I asked about this at my local nursery - what could I do to remove the ants from my peony buds? The gentleman recommended regular ant killer sprinkled around the base. Then I mentioned the problem at my bunco group. My neighbor nearly jumped out her chair and said "NO - it's ok! They are eating the sweet wax on the flower!"
Well, she's right! Apparently ants enjoy eating the sweet waxy coating over the buds.
So I have relented and allowed the ants to enjoy their buffet...and look forward to the beautiful blooms :)