Recently, detection of discrete features in the X-ray afterglow spectra of GRB 970508 and GRB 970828 was reported. The most natural interpretation of these features is that they are redshifted Fe K emission complexes. The identification of the line emission mechanism has drastic implications for the inferred mass of radiating material and hence the nature of the burst site. X-ray spectroscopy provides a direct observational constraint on these properties of gamma-ray bursters. We briefly discuss how these constraints arise in the context of an application to the spectrum of GRB 970508.