Recent, counterintuitive findings regarding the stability of quasinormal modes (QNMs) suggest that random perturbations to the effective potential could stabilize the QNM spectrum. In this talk, we present results obtained from the investigation of a physically motivated scenario. Instead of random perturbations, we analyze the pseudospectrum of a Schwarzschild-like black hole deformed by the Rezzolla-Zhidenko (RZ) parametrization. Our main results show that the quasinormal spectrum of the RZ black hole is unstable, and its pseudospectrum does not exhibit the features associated with stable wave operators, directly contrasting the results from random perturbations. We corroborate these findings by computing the spectra under additional deformations and argue that when multiple perturbation sources are present, identifying the origin of the instability may be difficult.