All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
It is unlawful for the woman to travel for ‘Umrah or for any other purpose without being accompanied by a Mahram. Ibn ‘Abbaas narrated that the Prophet said while giving a sermon: “No man should ever stay in seclusion with a woman unless in the presence of a Mahram of that woman. And no woman should travel unless accompanied by a Mahram. A man stood up and said: 'O Prophet of Allah! My wife went on Hajj and I have already been registered for the battle of such and such.' Thereupon, the Prophet said: ‘Go and perform Hajj with your wife.’” [Al-Bukhari and Muslim]
Some Muslim scholars are of the opinion that the woman could travel without a Mahram provided she is accompanied by a trustworthy group of people and provided her trip is an obligatory one like Hajj. So, if ‘Umrah is obligatory on this woman and not supererogatory, then it is lawful for her to travel if accompanied by a trustworthy group of people. Anyway, this matter is a controversial one. No doubt that if she finds a Mahram to accompany her, then that would be safer and more appropriate and the right thing to opt for. Otherwise, she can (if she is pious and righteous) travel with a trustworthy company.
Allah knows best.