She is correct in that majority of the school of thought believe that the triple talaq is not permissible. It’s not part of the Quran or sunnah, but it a common practise in our south asian home.
However the scholars differed about whether it would mean it’s an irrevocable divorce. The Hanafi school of thought does believe that it’s an irrevocable divorce. Therefore she can not reconcile with husband.
Triple talaq is the most disliked way of divorce that's why it is not part of Quran and Sunnah. The Holy Quran has taught better ways of divorce.
As i said it depends on someone's belief. Baki Allah knows best. And He may shows us right path.
