Kitō-ryū seems to have originally been a continuation, or version of the Ryōi Shintō-ryū (良移心当流).
https://www.researchgate.net/publication/330426217_Kito-ryu_jujutsu_and_the_desolation_of_Kodokan_judo%27s_Koshiki-no-kata_-Remembering_Inoue_Shoji_1927-2018