The Project 8 collaboration aims to measure the absolute antineutrino mass scale from the distortion of the tritium beta decay spectrum near its endpoint. To this end, the collaboration has successfully established Cyclotron Radiation Emission Spectroscopy (CRES), a new frequency-based approach to detect electrons and determine their kinetic energy. Since the neutrino mass is determined from a modification of the shape of the tritium spectrum near its high energy endpoint, it is essential to quantify any dependence of the electron detection efficiency on energy or, equivalently, frequency. Incorporating this dependence in the analysis is crucial for an accurate measurement of the endpoint and the extraction of the neutrino mass. In this talk, I will present how the detection efficiency in the Project 8 Phase II experiment is measured and demonstrate its impact as systematic error source on the spectrum analysis of the first tritium spectrum recorded with CRES.