The propagation of very energetic gamma-rays at GeV–TeV energies over cosmological distances is mainly affected by pair-production on the soft background photon field. The resulting energy dependent absorption is sensitive to the level of background photon field present along the line of sight as well as to possible modifications of the pair-production process. In this study, we focus on the latter aspect by fixing the absorption to the guaranteed level by invoking a minimum model for the background photon field. The result of the study suggests (at the level of 4.2 standard deviations) that the intrinsic spectra (after correction for absorption) show a significant upturn at the transition from optically thin to optically thick. The observation is not explained by known systematic effects related to the instrument (e.g. energy scale, spectral bias). By construction, neither the intrinsic source spectra nor the background photon field can be responsible for the observed effect unless either an un-realistic fine-tuning of the sources or a substantially lower level of the background light below the guaranteed level is realized in nature. We conclude, that the origin of the observed effect is most likely related to an anomaly of the pair-production process similar to the effect predicted in the case of a pseudo-scalar (axion-like) field.