We study the impact of the top quark mass renormalized in the $\overline{\text{MS}}$ scheme on the $\text{t}\overline{\text{t}}$H production cross-sections as an alternative to theory predictions with the conventionally used pole mass scheme. The differential cross-sections at next-to-leading order in perturbative QCD with stable top quarks show a moderate decrease in scale uncertainties for the $\overline{\text{MS}}$ mass renormalization scheme compared to the on-shell one. The shape of the differential distributions is not affected much, the largest differences being observed in the invariant mass distributions of the $\text{t}\overline{\text{t}}$ and the $\text{t}\overline{\text{t}}$H systems.