According to my knowledge, this hadith also proves that just as Hajj is obligatory, Umrah is also obligatory, because the Prophet Muhammad (peace be upon him) has clarified that for women, just as performing Hajj is necessary, performing Umrah is also necessary.

Umm al-Mu’minin Sayyidah Aisha (may Allah be pleased with her) narrates that I asked,“O Messenger of Allah, is jihad also obligatory upon women?”He (peace and blessings be upon him) replied:“There is such a jihad obligatory upon them in which there is no fighting; that is Hajj and Umrah.”Imam Abu Bakr (may Allah have mercy on him) says that in your statement that such a jihad is obligatory upon them in which there is no fighting, and you informed them that the obligatory jihad upon them is to perform Hajj and Umrah, there is evidence in this that Umrah is obligatory just like Hajj. Because the apparent meaning of your statement ‘alayhinna’ (upon them) is that it is obligatory upon them, because it is not correct to say this for a voluntary act of worship that it is ‘upon a person’. (This is only said when the obligation of something is intended to be conveyed.)