All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
You did not tell us whether your wife found the thread of blood after her regular period of menstruation or during it. If she found it after her regular period of menstruation, her circumambulation in the state of purity after cessation of menses is valid even if blood flowed after that. Her circumambulation is also valid if she had Ghusl after she had made sure that her menses terminated by inserting cotton swabs (or Q-tips) in her vagina and taking it out with no traces of blood over it, even if her usual duration of menses was not over yet.
This is based on considering the days when the blood flowed as the days of menstruation, and the days when menses was absent as the days of purity.
However, if the cessation of blood had not occurred before she had Ghusl, then she made Tawaaf during menses. This case is contested among scholars. The majority of them maintain that Tawaaf is invalid, whereas others said that it is valid and that a sheep must be slaughtered, according to Imaam Ahmad or a camel is to be slaughtered, according to Abu Haneefah .
Based on the view of scholars who think that her Tawaaf is invalid, your wife is still in the state of Ihraam and is required to avoid all Ihraam violations until she goes to Makkah to perform Tawaaf then Sa‘y, after which she would have completed her Hajj and comes out of the state of Ihraam.
However, we believe that your Tawaaf and Sa'y were valid, but it is better to be on the safe side and slaughter a sheep.Allaah Knows best.