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Sub-TeV or TeV γ -rays have been convincingly detected in the afterglows of some gamma-ray bursts (GRBs). The relativistic jet associated with GRBs may be surrounded by a cocoon and thus the thermal photons of the cocoon pervading the emission region of the jet can be upscattered to the very-high-energy regime (e.g., sub-TeV/TeV) by the electrons in the jet. In this scenario, the electrons in the jet cool down and thus the jet emission in the low-energy regime, e.g., the X-ray or optical, may be suppressed. In this paper, we study the effect of the cocoon's thermal photons on the jet emission in the low-energy regime. We find that the jet emission in the low-energy regime is significantly suppressed when the emission region of the jet is just encircled by a hot cocoon. Correspondingly, there is a sharp decay in the light curves of the jet emission in the low-energy regime, which can be understood to signify strong TeV emission in GRBs. Since the radius of the cocoon expands with the observer time t obs, the suppression of the jet emission in the low-energy regime may be relieved and thus the light curves of the jet emission would return to those of emission without a cocoon-external inverse-Compton cooling effect. For a long-lasting jet with power ∝ (1 + t obs / t c) α , an internal plateau followed by a sharp decay may generally appear. [ABSTRACT FROM AUTHOR]