Yadayim, Chapter Three, Mishnah Three
1) The straps of the tefillin [when connected] with the tefillin [boxes] defile the hands.
2) Rabbi Shimon says: the straps of the tefillin do not defile the hands.
Section one: Tefillin boxes have scrolls of Scripture in them. Therefore, they clearly would defile the hands. According to the first opinion, the straps do as well, as long as they are tied to the tefillin boxes.
Section two: Rabbi Shimon says that the straps do not defile the hands, since they are only connected to the boxesthey don’t have the scrolls in them.