We discuss the effect on the transient dynamics of the Richtmyer–Meshkov instability due to small-scale perturbations introduced by a set of solid circular cylinders located along the material interface. The arrangement of the cylinders mimics (in a two-dimensional domain) the presence of the solid supporting grid wires used in the formation of the material interface in an experimental setup. The numerical experiments are performed by utilizing an embedded boundary adaptive mesh refinement method. We quantify the effect of introducing the cylinders on the mixing layer growth and the mixedness level and qualitatively demonstrate the effect of the perturbation introduced by the cylinders on the mixing layer structure. We empirically model the effect of the solid cylinders based on their diameter and find that the effect of the cylinders on the mixing layer growth is a linear function of the cylinder diameter. The linear model allows us to predict the change in the mixing layer growth within a ±10% range, except for very small ratios of the initial perturbation amplitude of the density interface to the cylinder diameter.