  We study the momentum space representation of energy-momentum tensor
two-point functions on a space with a planar boundary in $d=3$. We show that
non-conservation of momentum in the direction perpendicular to the boundary
allows for new phenomena compared to the boundary-less case. Namely we
demonstrate how local contact terms arise when the correlators are expanded in
the regime where parallel momentum is small compared to the perpendicular one,
which corresponds to the near-boundary limit. By exploring two-derivative
counterterms involving components of Riemann tensor we identify a finite,
scheme-independent part of the two-point function. We then relate this
component to the conformal anomaly $c_\partial$ proportional to the boundary
curvature $\hat{R}$. In the formalism of this paper $c_\partial$ arises due to
integrating out bulk modes coupled to the curved space, which generate local
contributions the effective action at the boundary. To calculate the anomaly in
specific (free-field) examples, we combine the method of images with Feynman
diagrammatic techniques and propose a general methodology for perturbative
computations of this type. The framework is tested by computing $c_\partial$ on
the explicit example of free scalar with mixed boundary conditions where we
find agreement with the literature.
