Maxwell's demon is the quintessential example of information control, which is necessary for designing quantum devices. In thermodynamics, the demon is an intelligent being who utilizes the entropic nature of information to sort excitations between reservoirs, thus lowering the total entropy. So far, implementations of Maxwell's demon have largely been limited to Markovian baths. In our work, we study the degree to which such a demon may be assisted by non-Markovian effects using a superconducting circuit platform. The setup is two baths connected by a demon-controlled qutrit interface, allowing the transfer of excitations only if the overall entropy of the two baths is lowered. The largest entropy reduction is achieved in a non-Markovian regime and, importantly, due to non-Markovian effects, the demon performance can be optimized through proper timing. Our results demonstrate that non-Markovian effects can be exploited to boost the information transfer rate in quantum Maxwell demons.