Is scratching skin to the point where it leaves a temporary mark (red or white) a problem on Shabbos?
It is permitted. The reason the persons skin become temporarily red or white is due to the effect that the scratching has to the cirulation of the blood in the area that was scratched, and not because smoe blood has detached itself from the flesh. Therefore it isn’t considered mileches shochet. It is also not tzoveiah, because it doesn’t last at all, and you are not doing it in order to color the skin. This would be similar to pinching a child’s cheek, (of course not to hurt him) and his cheek became red as a result. The poskim say that it is permitted for the above reasons.
M:B Shar Haztion 303-65, Toldos Shemuel 3- mitzva 33 Tzoveiah 6, Chut Shani Tzoveiah- Hosafos 84.