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 was reported in Sunan An-Nasaa'i on the authority of Abu Hurairah that "The Messenger of Allah said: ‘If a woman goes out to the Masjid, let her perform Ghusl to remove perfume as she would perform Ghusl to remove Janabah (impurity following sexual activity).’” This is interpreted to mean that ghusl is recommended not obligatory according to the view of scholars. Or that what is meant by performing Ghusl in this case, is washing the part from her body that has perfume.
Al-Manawi said in Faydh Al-Qadeer: “(If a woman goes out) which means that if she wants to go out (to the Masjid), or somewhere else first (she has to perform Ghusl) this is recommended (to remove perfume) if she used perfume (as she would perform Ghusl to remove Janabah) if the perfume is all over her body; otherwise, she washes the part of the body that is perfumed only, as what is required is achieved by this.” [End of quote]
As for her prayers, they are valid, but she is sinful because of her going out wearing perfume, not wearing Hijab, and wearing tight clothes. She must repent of this deed and maintain the Islamic Hijab with its well-known conditions.
For more benefit on the evidence for Hijab and its conditions, please refer to Fatawa 81554, 83765, 83702, 81494, 354259 and 83033.
Allah knows best.