When estimating time-variable gravity field models from GRACE Follow-On data, a set of a priori given background force models is introduced in the processing to enable the computation of monthly snapshots of spherical harmonic coefficients representing the state of the Earth’s gravity field. The to-be-estimated spherical harmonic series has to be truncated at a certain point, for GRACE Follow-On commonly at degree and order 96, and one of the background models is usually a model for the gravity field itself, which is used to reduce higher frequency static gravity field signal to avoid aliasing (contained in degrees above 96). In this study we take a look on the influence of different strategies to treat the high degree gravity field signal in monthly gravity field solutions from GRACE Follow-On data. We estimate temporal gravity fields with fixed high degrees of different a priori background gravity field models, and opposed to this, we also co-estimate static spherical harmonic coefficients from degree 97 up to degree and order 160 from 51 months of GRACE Follow-On data along with the monthly snapshots to enable a consistent handling of correlations between time-variable and static gravity field coefficients. The observation noise modelling of the data is handled by an empirical covariance estimation for the noise based on post-fit residuals between the final GRACE Follow-On orbits, that are co-estimated together with the gravity field, and the observations. Since the post-fit residuals, amongst other things, depend on the choice of the background force models they are a potential carrier of a priori information into the final solution. The results show that a formal correlation between the time-variable and static gravity field coefficients is almost non-existent, and also the empirical covariance model has only minor impacts on this correlation. Only a poor choice of the background gravity field requires a prior or co-estimation of the static gravity field.