A broad statistical study addresses for the first time an evolution of ultra-low frequency (ULF) waves/fluctuations in the terrestrial foreshock around the Moon generated through the interaction between the back-streaming particles reflected from the bow shock and the incoming solar wind. They propagate sunward but are convected by the solar wind flow back toward the bow shock and their amplitudes grow. However, our study shows that waves could be growing as well as decaying towards the bow shock under the quasi-radial interplanetary magnetic field. We demonstrate that the statistically determined growth rate is positive and larger for compressive variations of the density and magnetic field strength than for its components. We show that even if a possible influence of the Moon and its wake is excluded, the growth rate is decreased by non-linear effects leading to saturation of the wave amplitude.