Breaking matzah into soup
Kneidlach are avoided by some until the 8th day of Pesach
Not eating gebrochts is a chumrah, a stringency, observed by some Ashkenazi Jews, particularly Chasidim, during Pesach. Non-gebrochts eaters do not eat matzah balls, matzah brei, matzah pizza, matzah croutons, or matzah anything that has come into contact with water.
Gebrochts means "broken" in Yiddish, referring to the broken pieces of matzah that people would put in their soup. The custom of not eating them seems to have become widespread in the 18th century. It is mentioned in the Shulchan Aruch Harav of the first Lubavitcher Rebbe, Rav Shneur Zalman of Liadi.
The practice orginated in a concern about raw flour in matzah. Once flour has been mixed with water and baked into matzah, it is no longer susceptible to leavening, becoming chametz. However, if clods of flour were not fully mixed with water before baking, then they could become leavened subsequently, if the matzah came into contact with water (or chicken soup). So some groups decided not to eat matzah that had contact with water.
The custom of not eating gebrochts does not apply on the eighth day of Pesach, which is rabbinic in origin. On that day, non-gebrochts eaters can go wild and dip their matzah into anything that kashrut and good manners allow.