We study star formation (SF) quenching of satellite galaxies with M _* > 10⁷ M _⊙ within two low-mass groups (M _vir = 10^12.9 and 10^12.7 M _⊙) using the NewHorizon simulation. We confirm that satellite galaxies (M _* ≲ 10¹⁰ M _⊙) are more prone to quenching than their field counterparts. This quenched fraction decreases with increasing stellar mass, consistent with recent studies. Similar to the findings in cluster environments, we note a correlation between the orbital motions of galaxies within these groups and the phenomenon of SF quenching. Specifically, SF is suppressed at the group center, and for galaxies with M _* > 10^9.1 M _⊙, there is often a notable rejuvenation phase following a temporary quenching period. The SF quenching at the group center is primarily driven by changes in SF efficiency and the amount of gas available, both of which are influenced by hydrodynamic interactions between the interstellar medium and surrounding hot gas within the group. Conversely, satellite galaxies with M _* < 10^8.2 M _⊙ experience significant gas removal within the group, leading to SF quenching. Our analysis highlights the complexity of SF quenching in satellite galaxies in group environments, which involves an intricate competition between the efficiency of SF (which depends on the dynamical state of the gas) on the one hand, and the availability of cold dense gas on the other hand. This challenges the typical understanding of environmental effects based on gas stripping through ram pressure, suggesting a need for a new description of galaxy evolution under mild environmental effects.