The article by J. Rocha de Faria et al. under discussion is concerned with the evaluation of the perturbation undergone by the potential energy of a domain $\Omega$ (in a 2-D, scalar Laplace equation setting) when a disk $B_{\epsilon}$ of small radius $\epsilon$ centered at a given location $\hat{\boldsymbol{x}\in\Omega$ is removed from $\Omega$, assuming either Neumann or Dirichlet conditions on the boundary of the small `hole' thus created. In each case, the potential energy $\psi(\Omega_{\epsilon})$ of the punctured domain $\Omega_{\epsilon}=\Omega\setminus\B_{\epsilon}$ is expanded about $\epsilon=0$ so that the first two terms of the perturbation are given. The first (leading) term is the well-documented topological derivative of $\psi$. The article under discussion places, logically, its main focus on the next term of the expansion. However, it contains incorrrect results, as shown in this discussion. In what follows, equations referenced with Arabic numbers refer to those of the article under discussion.