I've been searching your various websites, but I can't find any reference to the above subject (disposal of Siddurim and Torah Scrolls). Is this a religious requirement, or is it one of the myriad customs that have been hallowed over the centuries?

Any Hebrew name of God is forbidden to erase. From the Torah's exhortation to destroy idolatry, we learn out the prohibition not to destroy the name of God. (see Deuteronomy 12:3-4)

So you should bring Siddurim, Torah scrolls and any printed material to a box called Geniza (a.k.a. Sheimos).

Geniza is a box found in a synagogue where unusable holy objects are discarded. These include: old holy books or Torah scrolls that are falling apart or have become invalid; Tefillin or Tsitses that are defective; unwanted pieces of paper that has Holy words on it etc. When the box is full, it is taken to a place and buried.