Abstract: We consider the mixed topological-holomorphic Chern-Simons theory introduced by Costello, Yamazaki & Witten on a ℤ2 orbifold. We use this to construct semi- classical solutions of the boundary Yang-Baxter equation in the elliptic and trigonometric cases. A novel feature of the trigonometric case is that the ℤ2 action lifts to the gauge bundle in a z-dependent way. We construct several examples of K -matrices, and check that they agree with cases appearing in the literature.