In the story, "The Minister's Black Veil", how does the world outside the town react to the veil?

Very interesting question. It is clear that the black veil has both a positive and a negative impact on Mr. Hooper. We are told how the black veil distances him from his own village, and of course, especially his betrothed, Elizabeth, who breaks the engagement. However, it also has the "bonus" if such a term can be used of making him successful as a minister - a "very efficient clergyman", as the text puts it. The text states:

Strangers came long distances to attend service at his church, with the mere idle purpose of gazing at his figure, because it was forbidden them to behold his face. But many were made to quake ere they departed!

So it is clear that the veil makes him a novelty, but one which people are forced to take seriously, for the black veil strikes terror into visitors' hearts as well.

Note too, how the text says:

As the years wore on, shedding their snows above his sable veil, he acquired a name throughout the New England churches, and they called him Father Hooper.

The black veil therefore allows Mr. Hooper to really have an impact as a minister because of his "mysterious emblem", making him a "man of awesome power" and gaining many converts.