To first begin to understand how William Carleton's Wildgoose Lodge is a Postcolonial work, one must understand what Postcolonialsim is.
Postcolonialism is, according to eNotes,
the ways in which race, ethnicity, culture, and human identity itself are represented in the modern era, after many colonized countries gained their independence.
What this means is that literature of this genre deals with the cultural and political independence of people from a controlling authority.
That being said, the action of the text Wildgoose Lodge speaks exactly to that. Given that the text offers a historically based story of a Roman Catholic group which forces action against members who have betrayed the organization, the text epitomizes Postcolonial ideas based upon the fact that the group feels as if they are the controlling authority of its members. According to the group, anyone going against the group (or trying to show independence from the group) needs to be punished. The fact that the group ends up brutally murdering those who have betrayed the ideals shows the impact that controlling authorities have over people enacting, or trying to enact, independence.
Postcolonial literature simply examines the ideals behind oppression, identity and conflict of new and old ideals. The text is simply offering a point-of-view which establishes the conflicts associated with going against a dominant power and the repercussions which follow.