The low‐altitude, polar‐orbiting NOAA POES satellites are known to exhibit a spurious response to relativistic electrons in the proton telescope instrument of the Medium Energy Proton and Electron Detector (MEPED). This sensitivity has recently been used to identify relativistic electron precipitation from the radiation belts, but has heretofore remained unquantified. Monte Carlo simulations of the proton and electron telescopes were performed using the Geant4 code, and we derive the characteristic response of each instrument to isotropic proton and electron fluxes in the energy range 10 keV to 10 MeV. Geometric factors were found to agree with the nominal G ∼ 0.01 cm2sr response for target species (e.g. proton response of the proton telescope), while both telescope types also admit particles of the opposite species. The electron telescope is shown to respond to protons of energies 210–2600 keV with G ∼ 0.01 cm2sr. The proton telescope is similarly shown to exhibit a non‐negligible response to electrons, which although confined to the P1, P2, P3, and P6 energy channels, does attain an admittance of G ∼ 10−3 cm2sr near 460 keV and G ∼ 10−2 cm2sr near 1400 keV. These results confirm that the proton telescope can be used as an effective tool for detection of relativistic electron precipitation. Moreover, we suggest a method for combining the electron and proton telescope data to obtain corrected fluxes for both species which will facilitate the use of this instrument for quantitative studies of particle precipitation. Key Points Use of numerical modeling to quantify contamination of telescope instruments Use of proton telescope's P6 channel as indicator of relativistic electron flux Use of proton telescope's P6 channel to extend range of electron telescope