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, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
It seems to us – and Allah knows best – that applying this oil to the body is not included in the forbidden use of perfume for a woman when she goes out of her house since it does not have the smell of perfumes. The reason for forbidding women from applying perfume outdoors is because it may lead to arousing sexual desire (in the men who smell it). Al-Munaawi said, “...because she aroused men's lusts with her perfume.” [At-Tayseer bisharh Al-Jaami’ As-Sagheer 2/421]
Hence, you do not have to wash off the traces of this oil when you go to the masjid; however, if you could find another oil that has no fragrance, then that would be better and safer.
Allah knows best.