I would prefer it to be powered off incase i lean too hard on the screen and damage it. Its got a few greasy looking marks on it that arent easily removed as ive already tried a gentle wipe with a clean cloth. Using my jet wash sounds like a great idea @Ben Daniel Grant lol
With the ignition off, hold down the menu button on the centre console. That would power it in and just use a microfiber cloth to wipe it. No need to out any cleaning fluid. Mine was only dusty and used a mf cloth and that resolved my problem..
I use a clean piece of kitchen towel and a tiny drop of handwash liquid on my iPad. Just work it carefully until the liquid has disappeared, then polish with another paper towel.
But I wouldn't expect the MMI screen to be greasy like an iPad, so probably just need the MF as suggested. But you do mention grease, so maybe do need a bit of gentle de-greasing.