All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Wiping over the head is one of the obligatory acts of ablution, but the scholars differed as to the amount that is sufficient in wiping it; the view that we adopt here in Islamweb is that it is obligatory to wipe over the entire hair.
However, the matter is easier for a woman than for a man; therefore, many scholars are of the view that she wipes some of her hair during ablution.
Al-Mughni, authored by Ibn Qudaamah reads: “Among the scholars who said that she is only required to wipe over part of her hair is Al-Hasan, Ath-Thawri, Al-Awzaa’i, Ash-Shaafi’i, and the scholars of the Hanafi School, but the preponderant view according to Imam Ahmad for a man is that it is obligatory to wipe over the entire hair, and that it is sufficient for a woman to wipe the front of her head. Al-Khallaal said: The relied-upon opinion in the Hanbali School (i.e. the view of Imaam Ahmad) is that if she wipes over the front of her head, then it is sufficient for her. Muhanna said: Ahmad said: I hope that the matter for a woman in wiping her head is easier. I said to him: Why? He said: ‘Aa’ishah used to wipe over the front of her head.’” [End of quote]
Based on the above, if you wipe over that small hair tie, then there is no harm on you, but it is better to remove it if there is no difficulty or embarrassment in doing so.
Allah knows best.