When the deputation of the church approaches the Reverend Mr. Hooper to deal with "the mystery of his black veil" before it develops into what they worry might be a scandal, this group fails to "discharge its duties" and returns with no resolution to the mystery. 

After they experience the shock of seeing their minister step to the pulpit with a black veil shielding the lower part of his face, the members of the Reverend Mr. Hooper's congregation are greatly unnerved. His sermon on the topic of:

...secret sin and those sad mysteries which we hide from our nearest and dearest, and would fain conceal from our own consciousness, even forgetting that the Omniscient can detect them...

disturbs his congregation. They are frightened, and some feel that the minister, who now covers his face with a black veil, has "changed himself into something awful" or "gone mad." Others are secretly anxious, worried about what the minister knows that he must hide his face behind this dark veil.

Try as he may, the Reverend Mr. Hooper is unable to get his congregation to look within themselves behind their own figurative veils. To the members of his church, the veil becomes "the symbol of a fearful secret between him and them." After the deputation returns without any explanation, these men decide that the matter is too weighty for them. Consequently, they consider the idea of turning it over to a governing council of the churches, a council that may find something other than that which hides within the hearts of Mr. Hooper's congregation.