If the optical transient to gamma-ray burst (GRB) 970508 is indeed associated with the 8 May burst and is connected with the z = 0.835 absorption system reported by Metzger et al. (1997) [Natur, 387, 879], then either the GRB originated from an intrinsically very faint galaxy (L łesssim 0.01L$_*$) or it occurred at a large distance from a host galaxy (gtrsim25 h$_70$$^-1$kpc); a large offset of GRBs from galaxies would tend to favour the merging neutron star-neutron star (NS-NS) model (Mészáros & Rees, 1993 [ApJ, 405, 278]; Narayan et al., 1997 [ApJL, 395, 83]). Here we show that the properties of a suspected host galaxy, particularly its intrinsic brightness and comoving distance from the transient, can be constrained indirectly using the Mg II absorption features detected in the spectrum of the optical transient (Metzger et al., 1997 [IAUC, 6676]) by examining the galaxies in the vicinity of the optical transient from ground-based and Hubble Space Telescope (HST) images. This is an independent test of the brightness of GRB host galaxies irrespective of distances implied from logN-logP distributions. The spectral lines most likely arise from absorption by very underluminous galaxies; in which case the optical transient has revealed the presence of a population of intermediate-redshift dwarf galaxies.