Would buccal fat removal work to get rid of perioral mounds? (Photos)

I'm in my 50s. Mostly because I was bothered by the sagging around my mouth, I got a deep plane face lift. It was great for other things, but did not fix the mounds of (what appear to be) fat. When I asked about it, the dr said there wasn't any fat there when she did the surgery...but then, what is it? Is it sunken filler? Was she mistaken? Not much is improved if I pull the skin back. And is there anything that will correct it?