If one has a mouthwash bottle and a toothpaste tube that they've been using, do they need to get brand new ones for Pesach?
My concern is with any chametz that might have gotten onto the tube or into the bottle.
There is quite some discussion on whether toothpaste needs to be kosher for Pesach, but none I found focusing on chametz that would have gotten onto the tube or bottle. Poskim who permit regular toothpaste on Pesach do not mention this situation.
R Chaim Jachter cites R Yosef Dov Soloveitchik and R Moshe Feinstein stating that that toothpaste is not ra’ui li-achilat kelev (unfit for canine consumption) and thus one is permitted to use it on Pesach. And he writes here the same about R Herschel Schachter.
But since kosher toothpaste exists, and some are strict to use it, you should CYLOR as always.
Mouthwash is slightly different as many contain denatured alcohol which is chametz. R Jachter writes there is a debate whether one can taste an inedible item (mouthwash here) that one does not intend to swallow.
Rav Eider probably would forbid using mouthwash that has a “minty taste” or other pleasant taste (as opposed to a “medicine-like taste”), whereas Rav Hershel Schachter would likely permit it. Indeed, Rav Meir Bransdorfer (Teshuvot Knei Bosem 1:25) writes that mouthwash is permitted on Pesach if it has inedible Chametz only if it is not intended for eating or to enjoy the taste of it. This seems to imply that he would forbid using mouthwash unless it has a “medicine-like taste.” Rav Elazar Meyer Teitz also recommends to his Elizabeth, NJ community on Pesach not to use mouthwash that has a pleasant taste if it contains inedible Chametz.