Something came out of her following a gynaecological exam

Praise be to Allah.

I am not sure exactly what the nature of this exam is, but if that means a medical examination that is done via the vagina in order to treat the womb etc, and something comes out of the womb or the vagina as a result, such as blood, a discharge, etc., then the woman has to do the minor ablution (i.e., wudoo’). But if it is obvious that the blood that comes out is menstrual blood, such as if the examination coincides with her period, then she has to do ghusl.