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1. The Mishnah discusses what a woman may wear and what she may not wear in Reshus ha'Rabim on Shabbos.
2. A woman should not go out on Shabbos with strings of either wool or linen in her hair.
3. Two reasons are given for why this law (#2) does not apply to woven (thick) string.
4. There are two reasons why a woman may not wear a Katla on Shabbos.
5. While Rebbi Yehudah argues with the Tana Kama regarding strings of wool, he does not argue regarding strings made of hair.
A BIT MORE
1. She is not permitted to wear things that are considered a burden, but only things that are considered clothing or jewelry. Chazal also forbade some forms of jewelry lest the woman remove it in order to show her friends and then carry it four Amos in Reshus ha'Rabim.
2. Such strings are considered Chatzitzos when women immerse in a Mikvah, unless they are loosened. If a woman loosens them on Shabbos, she might carry them four Amos in Reshus ha'Rabim.
3. According to one version, Rav Huna explains that since it is thick and does not cause a Chatzitzah for immersion in a Mikvah, there is no concern that the woman will remove it and carry it. According to another (similar) version, it is because women keep these types of strings in their hair even when bathing.
4. The Beraisa states that it is forbidden to wear a Katla because it is a Chatzitzah (see #2). The Mishnah implies that if it is the type that is worn for beauty, it is also forbidden lest she remove it to show to her friends and carry it four Amos in Reshus ha'Rabim (Tosfos).
5. Since they do not close tightly around a woman's hair, everyone agrees that they are not Chotzetz for immersion and thus they may be worn outside on Shabbos.
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