Recently, I came across an old pair of tefillin peshutim of mine. They became un-fit for use years ago, and I have since replaced them with a sturdier pair, B''H. They aren't vintage, but they have seen better days for sure (peshutim don't hold up well in day-to-day use).
Understanding that they were a cheap pair, I was curious as to what the parchments looked like inside. I'd heard "horror stories" about cheap tefillin, and although I don't have the know-how to declare tefillin or mezuzos useable or not, I wasn't impressed with what I saw.
Anyway, when I opened up the tefillin shel yad and removed the parchment, something else fell out of the box. Upon inspection, I found that it was a small piece of cut retzuah (leather strap) that was stuffed in the compartment along with the parchment. I must say this was very unexpected.
I have never heard of any custom of putting a piece of retzuah in with the parchment. Why would there be a piece of retzuah in the compartment of the tefillin shel yad along with the parchment?