What is the reason for the tissues?
The first tissue is just that the nails shouldn’t fly around.
The 2 pieces of tissue is a minhag not sure the origin of it.
Though there’s a story of one of the previous belz’e rebbis (I think R’ Aron), that some people came to him complaining that Judaism & all the Halachas and Minhagim are to much for today’s generation & it’s time to ease it a little bit. The rabbi responded that they should give him a few days. After a few days the chasidim came back & he answered them that he was thinking of telling them that he agrees that the minhag of putting 2 chips of wood in the nails before discarding it could be stopped, but after further tinkering I changed my mind & Minhag Yosrael Torah & nothing should be done.
Don’t know the mekor of the story & sounds interesting that the Belz rabbi would even ‘think’ for a minute to not do any Halacha or minhag because yiddishkeit is to much…