At the start of each day, a gunslinger gains a number of grit points equal to her Wisdom modifier (minimum 1). Her grit goes up or down throughout the day, but usually cannot go higher than her Wisdom modifier (minimum 1), though some feats and magic items may affect this maximum.
Since the item explicitly calls out that it doesn't increase the maximum grit total, and it doesn't mention that the item would have its own reservoir of grit (like the Lucky enchantment), the extra grit per day has no effect on a normal gunslinger.
On the other hand, the Bushwacker Gunslinger Archetype has a modified grit ability, which would benefit from this item.
Trembling Grit (Ex):
At 1st level, at the start of each day, a bushwhacker gains grit points equal to her Wisdom modifier – 1 (minimum of 1). In addition to all the ways any gunslinger can regain grit, a bushwhacker who reduces a helpless or unaware opponent to 0 hit points or fewer also regains 1 grit point. This expands the way in which the bushwhacker gains grit points, so a bushwhacker who gains grit points in this way only gains 1 grit point for reducing a helpless or unaware opponent, not 2 grit points.
This otherwise works like the gunslinger's grit ability and alters that ability.
So the only gunslinger who can benefit fully from the Gunman's Duster would be the Bushwacker.