Anchorage is a great place to grow peonies, there are quite a few peony farms in Alaska, around Anchorage specifically. I am in Fairbanks and we have more sun here, I have never had a problem with sunburn in peonies. Maybe the p[lace where this particular peony grows gets too much heat (from a wall or something)? I agree with Jasmin, if three are green leaves it's better to leave them on the plant.
