  In this note we explore the variation of Hodge structures associated to the
orbifold Landau-Ginzburg B-model whose superpotential has two variables. We
extend the Getzler-Gauss-Manin connection to Hochschild chains twisted by group
action. As an application, we provide explicit computations for the
Getzler-Gauss-Manin connection on the universal (noncommutative) unfolding of
$\mathbb{Z}_2$-orbifolding of A-type singularities. The result verifies an
example of deformed version of Mckay correspondence.
