  Horsley and Simpson [Phys. Rev. A 88, 013833 (2013)] recently claimed that
the inhomogeneous Casimir pressure in a piston model is cutoff dependent, and
diverges when the cutoff parameter is removed ({\xi}->0). We demonstrate that,
there is a miscalculation in their derivation, and our correction results in a
cutoff independent Casimir pressure, based on first-order perturbation theory.
We give the general expressions of first-order perturbative inhomogeneous
Casimir energy which make it convenient to analyze the divergence problem or to
yield the Casimir force. The Casimir pressure contribution of parallel waves
(with wave vector parallel to the Casimir plates) together with the
non-commutativity of limit and summation operators, are discussed and found to
be useful for understanding the inhomogeneous divergence declared in another
paper [Phys. Rev. A 87, 043806 (2013)]. We should emphasize that we cannot yet
give an exact expression of inhomogeneous Casimir pressure beyond first-order
perturbation, which is worth future investigation.
