Can one use unscented or scented deodorant on tisha be’av? Can one brush teeth or gargle on tisha be’av? Its not for pleasure, but for cleanliness purposes?
It is permitted to use deodorant on Tisha Be’Av if the intention is only to remove or prevent body odor. This is based on the halachah that permits sichah, even on Tisha Be’Av, if it is for the sake of removing dirt (Orach Chaim 554, Biur Halachah s.v. sichah).
One may not brush teeth with water or gargle on Tisha Be’Av, as ruled by Rav Moshe Feinstein (see R. Shimon Eider’s Halachos of the Three Weeks, p. 19) and by the Minchas Yitzchak (Vol. 4, no. 109). However, the Mishnah Berurah (567:11) permits washing out the mouth for somebody who experiences “great discomfort.” In addition, the above-mentioned Minchas Yitzchak but permits brushing teeth with dry toothpaste.