It is controversial as to whether a pilonidal sinus is actually derived from a misdirected hair follicle or whether the hairs enter as a secondary process. (See first ref, a CMAJ article from 1956)
In any case, the task of the surgeon is to open the chronic sinus and remove "the accumulated pus, hairs and other debris." (see 2nd ref, Mayo clinic).
"balai de crin" (=sweeping of bristles) is rather a poetic way to describe this; the surgical term for the removal of extraneous material from a wound is "debridement."