  There is a proposal to search for a sterile neutrino in a few keV mass range
by the "Troitsk nu-mass" facility. In order to estimate sterile neutrino mixing
one needs to make precision spectrum measurements well below the endpoint using
the existing electrostatic spectrometer with a magnetic adiabatic collimation,
or MAC-E filter. The expected signature will be a kink in the electron energy
spectrum in tritium beta-decay. In this article we consider the systematic
effect of electron backscattering on the detector used in the spectrometer. For
this purpose we provide a set of Monte-Carlo simulation results of electron
backscattering on a silicon detector with a thin golden window with realistic
electric and magnetic fields in the spectrometer. We have found that the
probability of such an effect reaches up to 20-30\%. The scattered electron
could be reflected backwards to the detector by electrostatic field or by
magnetic mirror. There is also a few percent probability to escape from the
spectrometer through its entrance. A time delay between the scattering moment
on the detector and the return of the reflected electron can reach a couple of
microseconds in the Troitsk spectrometer. Such estimations are critical for the
planning upgrades of the detector and the registration electronics.
