The Questioner: Is the ruling of wiping over the ghutrah and kufiyyah the same as wiping over the ʿimāmah (turban)? And is wiping over the ʿimāmah restricted only to that which is wrapped around the head, or must it go under the chin?
Shaykh Muqbil: There is no harm in [wiping over] the ghutrah, this is because the Prophet ﷺ wiped over the khimār. As for the kūfiyyah, I do not know that the Prophet ﷺ had wiped over the qalansuwah (the kufi or skullcap). [Furthermore,] it is not a condition that that the ʿimāmah be muḥannakah (wrapped or tied under the chin); for there is no evidence for this.
Refer to the book: Ghārat al-Ashriṭah (1/363)