Gamma-ray bursts (GRBs) are among the most luminous sources in the universe. The nature of their emission at TeV energies is one of the most relevant open issues related to these events. The temporal and spectral features inferred from the early and late emissions usually known as prompt and afterglow, respectively, can be interpreted within the context of the fireball model. The synchrotron self-Compton process is expected during the afterglow phase. We explain how the theoretical SSC light curves can be compared with the hypothetical upper limit located at z=0.3. We show the allowed parameter space of the microphysical parameters and density of the circumburst medium. The most restrictive results are obtained when the SSC process lies in the fast cooling regime.