You'll want to go into the full face makeup section, clicking on nothing won't get rid of it, so just click on some random full face makeup, doesn't matter which, then click back on none and it should be gone.
Ah, that's what happened, I clicked on 'none' and nothing happenned. Didn't think of applying some and removing it again, I figured only the chair could remove the bad makeup. Thanks Motoki.
I also had one (1!) success with a salesperson talking a customer into the chair the stylist was standing behind. Took a mere 3 sim hours, as profits plummeted.