distemper is a sort of indoor paint. It is basically made of ground chalk and glue size, where the size is made of boiled up horses hooves, mixed with hot water. It has a characteristic and not very pleasant smell. It can be tinted in pale colours. The "white" is a bit on the grey side as it is just chalk and brown glue. Luckily it has not been in common domestic use for 50 years or so, though some traditional architects or contractors might have specified it.
It is a very nasty surface to try to redecorate, as it falls off when you try to paint it. Furthermore, you can't easily strip it, as it is too hard to scrape, and does not wash off in cold water. It will however wash off with hot water and a scrubbing brush. You can imagine how difficult this is on a ceiling. I have heard of people spreading hot porage over ceilings to soften it
I have had it in an old house, and ended up having to use lining paper on the ceiling. I was able to wash it off the walls, hot, but it is a rotten job. I would not want it in my house unless I was rich enough to pay some other poor sod to redecorate, and if I didn't have to smell it.
Unlike most people, I have also mixed and applied it, as it was used on Stage Flats for scenery, and often had to wash it off the canvas for re-use. Luckily those days have gone.
If they are asking you to plaster over a distempered surface, I think you will have to hack it off or scutch it, as it will not bond. If they just want to paint it over your plaster, then it's their problem, just leave them a nice smooth, but not polished, surface as if they were going to emulsion it. it is dead matt. Accept no responsibility for adhesion of the distemper to your wall.
