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>~3 providing it is not too hot, likely between 10^5 K and 10^6.5 K, and moderately metal enriched, Z~0.2 Z_sun. 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.
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