Does the presence of a medium-sized piece of a siwak stick lodged between the teeth after prayer invalidate the ablution, if its presence was not known before performing the ablution?

The presence of leftover miswak or other residue stuck to the teeth or mouth does not harm the validity of wudu or ghusl, because rinsing the mouth (madmada) and inhaling water into the nose (istinshaq) are a Sunnah according to the majority of scholars. And even those who consider them obligatory do not stipulate that water must reach every part of the mouth and nose.