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Abstract We present results from a Keck/DEIMOS survey to study satellite quenching in group environments atz ~ 0.8 within the Extended Groth Strip (EGS). We target 11 groups in the EGS with extended X-ray emission. We obtain high-quality spectroscopic redshifts for group member candidates, extending to depths over 1 order of magnitude fainter than existing DEEP2/DEEP3 spectroscopy. This depth enables the first spectroscopic measurement of the satellite quiescent fraction down to stellar masses of ~10^9.5M_⊙at this redshift. By combining an infall-based environmental quenching model, constrained by the observed quiescent fractions, with infall histories of simulated groups from the IllustrisTNG100-1-Dark simulation, we estimate environmental quenching timescales (τ_quench) for the observed group population. At high stellar masses (M⋆ = 10^10.5M_⊙) we find that ${\tau }_{\mathrm{quench}}=2.4\begin{array}{c}+0.2\\ -0.2\end{array}$Gyr, which is consistent with previous estimates at this epoch. At lower stellar masses (M⋆ = 10^9.5M_⊙), we find that ${\tau }_{\mathrm{quench}}=3.1\begin{array}{c}+0.5\\ -0.4\end{array}$Gyr, which is shorter than prior estimates from photometry-based investigations. These timescales are consistent with satellite quenching via starvation, provided the hot gas envelope of infalling satellites is not stripped away. We find that the evolution in the quenching timescale between 0 <z<1 aligns with the evolution in the dynamical time of the host halo and the total cold gas depletion time. This suggests that the doubling of the quenching timescale in groups sincez ~ 1 could be related to the dynamical evolution of groups or a decrease in quenching efficiency via starvation with decreasing redshift.