I made some grease patties with EO's a couple of weeks ago.
I don't have a mite problem but i don't plan to use formic acid etc, so I want to discourage mites in other ways.
I realize it's a controversial subject amongst BK's (what isn't? lol), and people disagree on whether it's effective, but I like the concept and am willing to give it a try. I'm just a new BK, but my bees were already used to being treated with EOs where they came from, and seemed to be doing quite well health-wise.
I also think it may encourage more active grooming. At first, I put a couple of globs on the bottom board entrance, to the side. The bees that tasted it would eat for a minute or two, sometimes just touching it with their tongues, sometimes standing right on it. When finished, they would sit and groom themselves quite a bit before leaving.
i used recipes from this (admittedly outdated) site:
http://www.wvu.edu/~agexten/varroa/varroa2.htm#Notes
I used oils of wintergreen, lemongrass, and thyme. Mostly wintergreen. Careful not to make it too strong. I also added some honey to make it more attractive to them. I only put one small patty on the top of each hive's frames, on a round 2 1/2" diam. piece of stiff paper. I take a glob about the size of a golf ball and flatten it onto the paper. After 10 days they are about gone and I will keep replacing them. I keep enough for several sets of pattie in a baggie in the fridge, and I made up the rest into equal baggies and put those in the freezer to take out one at a time.
My bees were a little hesitant the first couple of days, but now they line up all around the patty like it was a buffet table, and seem to enjoy eating it.
Yes, i know some think grease patties and/or essential oils are useless or worse. But oh well, we all have our beliefs.
I was feeding HoneyBHealthy in syrup to my bees when they first arrived (HBH has essential oils of spearmint and lemongrass), but now that nectar season is on, they won't touch syrup. But they are liking the patties!

I won't use them when I have honey supers on... but that will be a while yet since I just put their second deeps on a few days ago.