The braisa on 57b says that this headband called איסטמא which is used to help contain hairs that can't be contained by the standard head covering, is not a problem of shatnez. R. Shimon adds that it can be worn by a kalla and doesn't violate the gezeira that after the destruction of the beis hamikdash brides cannot wear crown-like head pieces. Regarding the shatnez issue, there is a machlokes between Rashi and Tosafos. Rashi says that it is made from a felt material that has never been spun into strings and woven. It is just flattened fibers that are held together and therefore not a violation of shatnez. Tosafos disagrees because even on felt there is a Rabbinic prohibition. Therefore, Tosafos says that since it is a coarse material, in conjunction with it being felt and not proper threads, there isn't even a Rabbinic prohibition. According to both these approaches it is very understandable why it wouldn't be a violation of עטרות כלות since it is made of material in a very inferior manner and certainly doesn't contain any type of precious metals or stones. The Shulchan Aruch 561:4 even permits crowns made of regular material so long as there are no precious metals in it.
However, Tosafos d.h. v'eina, writes that it is a standard cloth (maharsham says the term muzhav is a mistake and should say צבוע), but has sewn into it all sorts of precious stones, jewels and pearls. Being that the cloth is only there to help contain the precious stones, it is batul to the stones and doesn't qualify as a garment. This is why there is no problem of shatnez and it is also not susceptible to tu'mas nega'im. Tosafos apparently holds that even though the garment part of it is made like a regular garment that is spun and woven, and is soft, it would still not be a problem of shatnez since it is batul to the stones that are on it. Based on this, Rav Yitzchok Isaac Chaver (back of vilna shas) says that if one has a silver atara that is attached to a linen or even shatnez cloth, they may sew it on to their tallis and it will not be a violation of shatnez since the cloths is batul to the silver. Rav Moshe (dibros, heara 5, pg 376) wonders why this Tosafos isn't cited by the poskim. He assumes that even if this is what Tosafos means, since it isn't cited by the poskim, one cannot rely on this halacha l'ma'aseh.
The question that bothers me is, if the Aruch is correct that this head band is made from precious stones and metals, why would it not be a violation of עטרות כלות. It is one thing to permit head pieces made from materials, even if not just felt as Rashi describes, but once it will have precious stones (and Tosafos implies that gold is also sewn into it, even if the actual beged is not gold), it should be forbidden for a kalla to wear? Perhaps the rationale of R. Shimon for it not being a violation of the gezeira against crowns for brides is not based on how it is made but rather where on her head it is worn. Perhaps he holds that since it is worn below the head covering and not on the top of her head, it wouldn't qualify as a "crown" - וצריך עיון. Another possible explanation can be based on the Taz 361:6 who writes that the gezeira on crowns is only when they are made specifically for the bride. Based on this he permits using the silver crowns from the shul which was the custom in his time. Being that the איסטמא is not made for a bride, it would be permitted.