  In this paper we investigate gravitational waves production during the Big
Bounce phase inspired by the Loop Quantum Cosmology. We consider the influence
of the holonomy corrections to the equation for tensor modes. We show that they
act like additional effective graviton mass, suppressing gravitational waves
creation. However, this effects can be treated perturbatively. We investigate
the simplified model without these corrections and find its exact analytical
solution. For this model we calculate a spectrum of the gravitational waves
from the Big Bounce phase. The obtained spectrum decreases to zero for the low
energy modes. Based on this observation we indicate that this effect can lead
to the low CMB multipoles suppression and gives a potential way to test Loop
Quantum Cosmology models. We also consider a scenario with a post-bounce
inflationary phase. The obtained power spectrum gives qualitative explanation
of the CMB spectra, including low multipoles suppression. This result is a
challenge to construct a consistent bounce+inflation model in the Loop Quantum
Cosmology.
