Her period became longer because of the IUD
If the period becomes longer because of the IUD and the bleeding follows on from the period, then it is all menses, such as if her period is usually seven days but increased to eleven days.
But if the bleeding stopped after the seven days, and she was certain that she had become pure, then she bled for four more days that was different from her usual menstrual bleeding, and that was because of the IUD, then these four days are not regarded as menses, rather they are istihaadah (irregular vaginal bleeding).
Similarly, if it is proven medically that the blood was irregular bleeding and not menses, then it is istihaadah.
If a woman does not fast when she sees blood because she thinks that it is menstrual bleeding, then it becomes clear to her that it was istihaadah, she does not have to do anything apart from making up the days that she did not fast.
Conclusion: If it is proven that these days were not menstrual bleeding, then she does not have to do anything apart from making up those days.
And Allaah knows best.