Does a woman have to repeat purification if she sees a brownish discharge two days after her seven-day menstrual period, knowing that this is the first time this has happened to her?

The brown color mentioned is considered "kudra" (a brownish discharge) and is not considered menstruation unless it is connected to blood and occurs during the usual time of one's period.

Therefore, it is not necessary to re-perform ghusl (ritual purification bath) due to the exit of this drop. It suffices to purify the body and clothing and perform wudu (ablution).