Hi,
I'm wondering if you may have an infestation of thrips. Is the 'powder' on the petals below the pollen sacs? If so, you probably have thrips, which are small bugs that eat the pollen and cause some to spill onto the petals.

If the mildew is on upper petals too, you have a different problem. I have only experienced PM on leaves but not on blossoms.

So, knowing where the patches show up would be helpful.

Barbara

It could be Botryis blight. Pinch off the blooms. The spores can become airborne and affect other plants.

Nancy

One way to tell if you have thrips is to gently blow on the blossoms - sometimes you can see the bugs scurry out of the pollen sacs.

Many, many thanks to all who have answered!
The "powdery mildew" (if that is what it is) is confined to the petals. Specifically the area on the petals that is basically horizontal, or flat. It is not down into the heart of the flower. It is not on the leaves at all.
The "whatever it is" does not adversely affect the flowers at all. They do not wither or anything like that. It is just these areas on the petals that is actually not powdery at all and will not come off if you rub it. I have removed the flowers tardily on earlier occasions and most recently promptly as soon as the "whatever it is" re-appeared. I can't seem to get rid of it but other than doing what I have described everything else is normal and healthy. No evidence of any insects at all.