If a person noticed a while after putting on Tefilin shel Yad that a small part of his shirt is under his retzuah (straps), when he removes it, does he say a new bracha due to the chatzitzah?
Thank you for your question.
Before answering your question, it is noteworthy that there is a difference between a chatzitza under the part of the strap that is actually tying the tefillin, to the other parts of the strap that are merely customary (such as the 7 times that the strap is wrapped around the arm). According to the Mishna Berura (27-16), we don’t have to be concerned with a chatzitza under the part of the strap that is wound around the arm 7 times, however many people nevertheless switch their watch to the other hand while they have their tefillin on. Therefore, if the part of the shirt was between that part of the strap there is no concern at all.
Even if the shirt was between the part of the strap that is tying the tefillin to your arm, b’dieved you will not have to make another bracha. The reason is because the opinion of the Rashba is not to be concerned with a chatzita, and although we don’t pasken like the Rashba, regarding saying another bracha, we will still say that it is controversial and you would not make another bracha.
Piskei Teshuvos 27-8.