The intrinsic X-ray emission of Gamma-Ray Bursts ( GRBs ) is often found to be absorbed over and above the column density through our own galaxy . The extra component is usually assumed to be due to absorbing gas lying within the host galaxy of the GRB itself . There is an apparent correlation between the equivalent column density of hydrogen , N _ { H,intrinsic } ( assuming it to be at the GRB redshift ) , and redshift , z , with the few z > 6 GRBs showing the greatest intrinsic column densities . We investigate the N _ { H,intrinsic } - z relation using a large sample of Swift GRBs , as well as active galactic nuclei ( AGN ) and quasar samples , paying particular attention to the spectral energy distributions of the two highest redshift GRBs . Various possible sample biases and systematics that might produce such a correlation are considered , and we conclude that the correlation is very likely to be real . This may indicate either an evolutionary effect in the host galaxy properties , or a contribution from gas along the line-of-sight , in the diffuse intergalactic medium ( IGM ) or intervening absorbing clouds . Employing a more realistic model for IGM absorption than in previous works , we find that this may explain much of the observed opacity at z \gtrsim 3 providing it is not too hot , likely between 10 ^ { 5 } K and 10 ^ { 6.5 } K , and moderately metal enriched , Z \sim 0.2 Z _ { \odot } . This material could therefore constitute the Warm Hot Intergalactic Medium . However , a comparable level of absorption is also expected from the cumulative effect of intervening cold gas clouds , and given current uncertainties it is not possible to say which , if either , dominates . At lower redshifts , we conclude that gas in the host galaxies must be the dominant contributor to the observed X-ray absorption .