  The formalism of linear response theory can be extended to encompass physical
situations where an open quantum system evolves towards a non-equilibrium
steady-state. Here, we use the framework put forward by Konopik and Lutz [Phys.
Rev. Research {\bf 1}, 033156 (2019)] to go beyond unitary perturbations of the
dynamics. Considering an open system comprised of two coupled quantum harmonic
oscillators, we study the system's response to unitary perturbations, affecting
the Hamiltonian dynamics, as well as non-unitary perturbations, affecting the
properties of the environment, e.g., its temperature and squeezing. We show
that linear response, combined with a quantum probing approach, can effectively
provide valuable quantitative information about the perturbation and
characteristics of the environment, even in cases of non-unitary dynamics.
