Q. Can one dispose of the small cardboard boxes in which the Esrogim are packed when one acquires them and also the long plastic carriers one uses for carrying the Lulav, by just throwing the into the waste cans?
A. Although these containers do not acquire any holiness at all, since they were not used for a mitzva themselves and in principle could be disposed in regular waste bins, Ginzei Hakodesh (20: 5, n. 9) quotes opinions that it is preferred if possible to dispose of the with some respect.
However, everyone agrees that care should be taken to remove any Tefilos and blessings that often are included in them.
Horav Shlomo Miller’s Shlit’a opinion is similar.
Rabbi A. Bartfeld as revised by Horav Dovid Pam, Horav Aharon Miller and Horav Chano