Polymer microgel particles decorated with redox-active functional groups are a new and promising object for electrochemical applications. However, the process of charge exchange between an electrode and a microgel particle carrying numerous redox-active centers differs fundamentally from charge exchange involving only molecular species. A single act of contact between the microgel and the electrode surface may not be enough to fully discharge the microgel, and partial charge states are to be expected. Understanding the specifics of this process is crucial for the correct analysis of the data obtained from electrochemical experiments with redox-active microgel solutions. In this study, we employed coarse-grained molecular dynamics to investigate in detail the act of charge transfer from a microgel particle to a flat electrode. The simulations take into account both the mobility of functional groups carrying the charge, which depend on the microgel architecture and the charge exchange between the groups, which can accelerate the propagation of charge within the microgel volume. A set of different microgel systems were simulated in order to reveal the impact of their characteristics: fraction of redox-active groups, microgel molecular mass, cross-linker content, cross-linking topology, and solvent quality. We have found trends in microgel composition leading to the most efficient charge transfer kinetics. The obtained results would be useful for understanding experimental results and for optimizing the design of redox-active microgel particles aimed at faster discharge rates.