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.
There is no harm for the woman to remove the mustache and beard from her face. She can remove it by any means, of shaving or picking. This is the opinion of the majority of the Muslim scholars. Imam Al-Tabari contradicted this opinion. He considered it as part of the unlawful picking of small hair, but the opinion of the majority of the Muslim scholars is most correct. Some of the scholars even made it obligatory for the women to remove this kind of hair.
Allah knows best.