Question: Am I allowed to wash up the dirty dishes from Shabbos on Tisha B’av afternoon?
Answer: The Shulchan Aruch (OC 554:9) writes that if one’s hands are dirty on Tisha B’av, one may wash off the dirt. The Mishna Berura (554:19) explains that washing one’s hands in this manner cannot be considered to be pleasurable bathing. Therefore, he writes that one who is cooking would be allowed to rinse meat, even though inevitably their hands will get wet.
Nonetheless, R’ Pesach Eliyahu Falk (Machazeh Eliyahu 1:87) demonstrates that one must avoid getting one’s hands wet as much as possible. One cannot bathe their children unless it is absolutely necessary. This applies even though the restriction against bathing does not apply to children. He quotes the Beis Yosef (OC 616) who explains that unlike feeding one’s children when one does not benefit oneself, by bathing one’s children, one’s own hands get wet. Therefore, one must not wash any dishes that were used to feed one’s children on Tisha B’av. As it is normal to wait a few hours before washing dishes, one should wait till after the fast.
However, this does not apply to washing dishes that were used prior to Tisha B’av, when doing so is akin to cleaning dirt off one’s hand. The Piskei Teshuvos (554:21) writes that ideally one should wash up in cold, rather than warm water, but R’ Falk writes that this is not necessary. Rather, he suggests that one wear rubber gloves.
In conclusion, one may wash one’s dishes from Shabbos on Tisha B’av afternoon even if one’s hands will get wet. One should wait to wash other dishes that were used to prepare food on Tisha B’av, or wear rubber gloves to prevent one’s hands from getting wet.