The detection of gravitational waves (GWs) with ground-based interferometers like the Laser Interferometer Gravitational Wave Observatory (LIGO) revolutionized our view of the Universe. Pulsar timing arrays (PTAs) like observed by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) will provide the community with an avenue for exploring the GW spectrum beyond what is capable with ground-based interferometers. Unlike LIGO, pulsars do not exist in an ideal environment where clever engineering can mitigate noise. With that being said, many of the dominant sources of noise in PTAs have been well modeled within NANOGrav. The impact of red spin noise (RSN), which may result from rotational instabilities in the neutron star itself, is particularly problematic because its effect on a PTA’s timing residuals could resemble the effects of a gravitational wave background (GWB). By simulating a PTA where each pulsar suffers from varying amplitudes of RSN and also has an underlying GWB we can attempt to recover the parameters describing the RSN to better characterize how these two signals could bias each other. We find regions of parameter space where the GWB and the RSN heavily bias each other. In these regions, RSN could masquerade as a GWB, or vice versa. However, we also find regions of parameter space that do not result in a biased recovery. Our work allows us to define the problematic regions of parameter space and draw conclusions about GWB recovery efforts in today’s operational PTAs.