  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.
