Microgels are confined to fluid interfaces in numerous applications, yet many aspects of the microgel-covered interface remain unclear. In this work, we use interfacial shear and dilatational rheology to study the effects of electrostatics on the mechanical characteristics of polyelectrolyte microgel monolayers at oil-water interfaces as a function of the microgel interfacial concentration. We find a clear correlation between the influence of charges on the mechanical properties of the monolayers and the influence of charges on their two-dimensional phase behavior. At lower microgel interfacial concentrations, the moduli of uncharged monolayers are larger than those of charged monolayers. Consistent with our previous findings on the phase behavior, here, the mechanical response of the interfacial layer is controlled by in-plane interactions of the microgels within the interface. At higher microgel interfacial concentrations, the moduli of charged monolayers are larger than those of uncharged monolayers. The mechanical response becomes dominated by out-of-plane interactions between the fractions of the adsorbed microgels further from the interface. Evidently, electrostatic interactions do not contribute directly to the mechanical response of the interfacial layer, that is, through charge repulsion, but indirectly through the difference in the swelling properties of uncharged and charged microgels. These results advance our understanding of how the charge-dependent microstructure of the interfacial layer affects its mechanical properties, which is not only important from a fundamental point of view but is also relevant to applications where polyelectrolyte microgels are used as responsive emulsion stabilizers.