Q. Is it correct that one should dismantle his Suka immediately after the end of the Yom Tov?
A. Nitei Gavriel (Sukos 103: 5, p. 476) indeed quotes from the Talmid of the Arizal, the Seder Hayom, that one should dismantle the Suka straight after the end of Yom Tov, since it shows then that the Suka was build only with the intention of the mitzva. However, he writes that just covering the Suka with a cover that protects from rain suffices. (See also similar in Chabatzeles Hasharon p. 871 and 820).
Doleh Umashke (p. 260) mentions the above question and quotes that the Gaon of Vilna would see to eat some chametz immediately at the end of Pesach, to similarly demonstrate that the avoidance of eating chametz before, was done only with the intention of keeping the mitzva of Hashem.
However, his own opinion is that he has not heard of that minhag and people don’t usually do it.
Horav Aharon Miller Shlit’a opinion is similar.
Rabbi A. Bartfeld as advised by Horav Shlomo Miller and Horav Aharon Miller Shlit’a