  We aim to understand the nature of the absorbing neutral gas in the galaxies
hosting high-redshift long-duration GRBs and to determine their physical
conditions. We report the detection of a significant number of previously
unidentified allowed transition lines of Fe+, involving the fine structure of
the ground term and that of other excited levels, from the zabs=3.969, log
N(H0)=22.10 DLA system located in the host galaxy of GRB 050730. The
time-dependent evolution of the observed Fe+ energy-level populations is
modelled by assuming the excitation mechanism is fluorescence following
excitation by ultraviolet photons. This UV pumping model successfully
reproduces the observations, yielding a burst/cloud distance (defined to the
near-side of the cloud) of d=440\pm 30 pc and a linear cloud size of
l=520{+240}{-190} pc. We discuss these results in the context of no detections
of H2 and CI lines in a sample of seven z>1.8 GRB host galaxies observed with
VLT/UVES. We show that the lack of H2 can be explained by the low
metallicities, [X/H]<-1, low depletion factors and, at most, moderate particle
densities of the systems. This points to a picture where GRB-DLAs typically
exhibiting very high H0 column densities are diffuse metal-poor atomic clouds
with high kinetic temperatures, Tkin>~1000 K, and large physical extents,
l>~100 pc. The properties of GRB-DLAs observed at high spectral resolution
towards bright GRB afterglows differ markedly from the high metal and dust
contents of GRB-DLAs observed at lower resolution. This difference likely
results from the effect of a bias, against systems of high metallicity and/or
close to the GRB, due to dust obscuration in the magnitude-limited GRB
afterglow samples observed with high-resolution spectrographs.
