Abstract: Recently, an improved quenching factor (QF) measurement for low-energy nuclear recoils in CsI[Na] has been reported by the COHERENT Collaboration. The new energy-dependent QF is characterized by a reduced systematic uncertainty and leads to a better agreement between the experimental COHERENT data and the Standard Model (SM) expectation. In this work, we report updated constraints on parameters that describe the process of coherent elastic neutrino-nucleus scattering within and beyond the SM, and we also present how the new QF affects their interpretation.