Responsa su Esodo 13:9

The source of the matter here is in Tractate Menachot 42b: “This, however, is a matter of dispute between Tannaim, for it has been taught: If a man overlaid [the tefillin] with gold or covered them with the skin of an unclean animal, they are invalid²⁷That the law of the Lord may be in thy mouth (Ex. 13:9), the tefillin should be made from that which is permissible for food; if with the skin of a clean animal, they are valid, even though he did not prepare it for this specific purpose. Rabban Simeon b. Gamaliel says, even if he covered them with the skin of a clean animal they are invalid, unless it had been prepared for this specific purpose²⁸Similarly the first Tanna and Rabban Simeon b. Gamaliel would differ as to the necessity for weaving the threads specifically for the purpose of zizith “.

As the Rosh thought there, towards the end of his statement, that the parchment, straps and the boxes, and compares them to the hide of the boxes, as they are also disqualified if they are not made to the specific task, so that one can generalize that he also explains that braitta as pertaining to the actual boxes; it does not seem to apply to the hide that is on the boxes at all.

In regards to hides from a ritually impure animal, he wrote ‘that were made from the hide of a ritually impure animal’, implying that the boxes were made from the hide of a ritually impure animal.