Shaykh Muhammad ibn ‘Uthaymeen (may Allaah have mercy on her) said: 

The ruling with regard to your wife is that she should stay until she becomes pure (i.e., her period ends and she does ghusl), then she should make up her ‘Umrah, because when Safiyyah got her period, the Prophet (peace and blessings of Allaah be upon him) said: “Is she keeping us (from leaving)?” They said: “She has already done tawaaf al-ifaadah.” He said: “Then let her set out.”  

The words of the Prophet (peace and blessings of Allaah be upon him), “Is she keeping us (from leaving)?” indicate that a woman who gets her period before doing Tawaaf al-Ifaadah has to stay until she becomes pure and then do tawaaf. The same applies to the tawaaf of ‘Umrah because it is one of the pillars or essential parts of ‘Umrah, just as Tawaaf al-Ifaadah is one of the essential parts of Hajj. If a woman who is doing ‘Umrah gets her period before she does tawaaf, then she must wait until she becomes pure and then do tawaaf.