The piece of retzuah (it can’t be a used piece since it has kedusha) may keep the retzuah from moving around within the maavarta but it usually doesn’t keep the Yud against the bayis so I don’t recommend it.
Please note that I didn’t specifically mention Beit El by name as a reliable online source, as while I’m sure they are very reliable, if I don’t know them personally then I can’t honestly mention them by name. I do know Hasofer so can mention them by name. Besides the 3 sources mentioned, there are a number of others that I understand are highly regarded.