For a woman, praying in the depths of her house has more reward than praying in the mosque. Some scholars mention that women attain the same reward praying at home as men get for praying in congregation. So yes definitely one can pray tarawih at home even when one is not a hafizah.
According to the majority of the fuqaha, tarawih prayer is a confirmed sunna with 20 rakahs. These acts of worship are just the means for us to draw closer to Allah Most High. The Prophet Muhammad (Allah bless him & give him peace) said, Anyone who stands in prayers during its nights with purity of belief and expectation of a reward, will have his previous sins forgiven." Also as other hadiths tells us, the rewards for good deeds and acts of worship are multiplied manifold during Ramadan
According to the consensus of Muslim scholars, Tarawih is not considered mandatory on either men or women. Rather, it is only considered a recommended act. There is no evidence in the sources to make it obligatory. As far as I know, no jurist or imam has expressed such an opinion.
Tarawih can be performed individually at home or at the mosque. If for some reason you cannot go to the mosque, you can pray Tarawih at home.
We know from the traditions that the wives of the Prophet (peace and blessings be upon him) and other companions often used to pray Tarawih at home. Some of them even opened the Qur'an and read from it while performing Tarawih.
Women and even children should attend it at the Mosque because it displays the unity among Muslims and cements their relationships.
