Q.  After Shavuos do the branches of the trees and flowers that were used for decorating the shul, have to be treated like the Schach or the Hoshanos after Sukos, and bury them properly?
A. On question 1882 we wrote: “Shulchan Aruch (O.H. 664: 8 and 21:1 and Shaarei Tzion ibid. 20) warn on not stepping on leftover mitzvos as leafs of Hoshanos or threads of tzitzis. Therefore Horav Shlomo Miller’s Shlit’a opinion is that leftover schach and arba’as haminim should not be thrown into the common garbage bin, since they were used for a mitzva. Rather they should be disposed in paper bags with the rest of leaves and branches that will end up being buried in land fills. They may also be double wrapped or bagged and then disposed off in the regular garbage.”
However, Horav Shlomo Miller’s Shlit’a opinion is that since decorating the shul with greenery is only a minhag and not a mitzva, the above restrictions do not apply.
Rabbi A. Bartfeld as advised by Horav Shlomo Miller and Horav Aharon Miller Shlit’a