Praise be to Allaah.
Menses does not prevent a woman from entering ihraam for Hajj
and ‘umrah, but it is haraam for her to circumambulate the Ka’bah until
after her menses ends. The Prophet (peace and blessings of Allaah be
upon him) said to ‘Aa’ishah (may Allaah be pleased with her) when she got
her menses before entering Makkah: “Do everything that the pilgrim does but
do not circumambulate the House until you become pure (i.e., your menses
ends). Agreed upon.
It is proven in Saheeh al-Bukhaari that when she
became pure, she circumambulated the Ka’bah and did saa’i between al-Safa
and al-Marwah. This indicates that if a woman gets her menses before doing
tawaaf, she should not do tawaaf and saa’i until she becomes pure.
Based on this, what you wife must do is wait until she
becomes pure, and then circumambulate the Ka’bah and do saa’i between
al-Safa and al-Marwah, then cut her hair. Then she will have completed her
‘umrah. And she does not have to offer a ransom for having gotten her menses
when she was in ihraam.
See also the answer to question no.
And Allaah knows best.