Could we throw out the cheap menorahs after Chanukah is over?
Thank you for your question.
My assumption is that you are not asking regarding baal tashchis, but if the menora is a mitzva object or not, and if it should go into shaimos. A menorah after one is finished using it, is considered tashmish d’tashmish or a mitzva, (lit. an item that was used in the past to service a mitva). The halacha of tashmish dtashmish may be thrown out regularly, however according to some poskim, if it looks like a mitzva item, such as a menorah, then it should not be thrown out in a degrading way. Therefore, you should wrap it in a plastic bag, and then put it in the garbage, so it won’t be lying mixed in together with the dirty garbage. It is important to mention that if the menorah says “הנרות הללו קודש הם”, then it needs to go into shaimos, because of the halacha that is written on it.
O:CH 21-1, Pri Megadim Mishbitzos Zahav O:CH 153-15, Ginzei Hakodesh 16-10, in the name of R’ N. Karelitz and R’ Eliyashov zt”l, and 9- ftnt. 2 in the name of R’ Eliyashiz zt”l that הנרות הללו needs to do into shaimos because it is part of a maamar chazal