What is the ruling concerning the prayers offered by the questioner during a period of three months, given that she was unaware that she needed to perform ghusl after the end of her menstrual cycle?

Murky discharge (Kudra) is not considered menstruation unless it is connected to menstrual blood or occurs during the days of menstruation. As for murky or yellowish discharge (Kudra or Sufra) after purification (Tuhr), it is not considered anything. The observation of murky discharge alone by a woman new to menstruation (Mubtada'ah) is a matter of scholarly disagreement, and the more preponderant opinion is that murky and yellowish discharge during the possible time of menstruation (Zaman al-Imkan) is considered menstruation. If the murky discharge was menstruation and you prayed out of ignorance of its ruling, then there is no blame upon you.