If the Universe was filled with a significant fraction of compact dark matter, gravitational lens echoes would be expected in the light curve immediately following a Gamma Ray Burst (GRB). Dark matter, acting as a lens, would cause some light rays from the GRB to arrive at a delayed time and hence such an echo should be detected in the background of the GRB. However, this would depend on the relative observer, lens and source orientation as well as the mass of the compact dark matter. Although the theory has been well established, no such gravitational echo has yet been detected in the light curves of a GRB. The non-detection of an echo in the background of the light curves of sources such as GRBs can lead us to improve limits on the nonexistence of compact dark matter within a specific mass range. Several GRBs from the FERMI satellite have been used in order to search for such echoes utilizing different statistical methods such as the Chi-square and the Anderson Darling test. Based on the present dark matter density parameter (0.3), the fractional density of compact dark matter lenses that should be found is computed and is then compared with the results obtained from the statistical tests. Preliminary results are presented limiting the existence of compact dark matter with a mass ranging from 105 to 1010.