Question: My younger son wears a “Tallit Katan” (Tzitzit garment). When I see that the Tzitzit strands become entangled, may I untangle them on Shabbat?
Answer: Before reciting a blessing on a Tallit or a Tallit Katan (Tzitzit garment), one must separate the Tzitzit strands from one another.
Nevertheless, if one sees the Tzitzit strands entangled on Shabbat, Hagaon Rabbeinu Yosef Haim zt”l writes in his Sefer Ben Ish Hai (Parashat Bereshit) that one may not untangle the strands and may only inspect them visually to sees that the Tzitzit are not invalid since untangling the Tzitzit is forbidden.
Maran Rabbeinu Ovadia Yosef zt”l writes in his Responsa Yabia Omer (Volume 5, Chapter 3) and in his Sefer Halichot Olam that the source for the ruling of the Ben Ish Hai is Maran Ha’Chida in his Kesher Gudal who writes that if the Tzitzit strands are entangled on Shabbat, they may not be untangled.
On the other hand, Maran zt”l points out that the first source we find for this law is in the Responsa Ginat Veradim (Kuntres Gan Ha’Melech, Chapter 65) writes explicitly that this prohibition only applies when the Tallit or Tzitzit is brand new and immediately after tying the Tzitzit strands, they became tangled in which case untangling them constitutes a forbidden work of putting “the finishing touches” on a job since the Tallit is unusable without first untangling the strands. However, if the Tzitzit strands were tied on the garment long before and the garment was used several times already and only later did the strands become entangled, there is no reason to prohibit gently untangling the strands from one another as this is not considered putting the “finishing touches” on the Tallit at all.
Maran zt”l proceeds to support his opinion with proofs from the great Poskim. Thus, halachically speaking, it is forbidden to untangle the Tzitzit strands of a brand new Tallit on Shabbat if they become tangled. However, a Tallit that has already been used worn and only later, its Tzitzit strands become entangled because of the laundry or any other reason, the strands may be untangled on Shabbat gently.