Using the hides of kosher animals
Chazal learned from the phrase "in order that Hashem's Torah be in your mouth" that Torah-related items (e.g. sefer Torah, tefillin) must be written on materials that are acceptable for the mouth - i.e. kosher. Accordingly, the parchment for the scrolls and the hides for the batim (the letter shin-part of Hashem's name-projects from the side of the shel rosh) must come from kosher animals. A halacha l'Moshe m'Sinai adds that the bayis for the shel yad and the sinews used to stich the tefillin closed must also come from a kosher animal. The retzuos straps must also come from a kosher animal. If there is a question about the origins of the retzuos straps it should be treated stringently, as if it was a d'oraisa.
(סעיף לז, ס"ק קסו וביה"ל ד"ה טהורים; וראה ביאורים ומוספים דרשו, 203)