Progenitor stars of long gamma-ray bursts (GRBs) could be surrounded by a significant and complex nebula structure lying at a parsec-scale distance. After the initial release of energy from the GRB jet, the jet will interact with this nebula environment. We show here that for a large, plausible parameter space region, the interaction between the jet blast wave and the wind termination (reverse) shock is expected to be weak, and may be associated with a precursor emission. As the jet blast wave encounters the contact discontinuity separating the shocked wind and the shocked interstellar medium, we find that a bright flash of synchrotron emission from the newly formed reverse shock is produced. This flash is expected to be observed at around ∼100 s after the initial explosion and precursor. Such a delayed emission thus constitutes a circumburst medium (CBM) phase in a GRB, having a physically distinct origin from the preceding prompt phase and the succeeding afterglow phase. The CBM phase emission may thus provide a natural explanation for bursts observed to have a precursor followed by an intense, synchrotron-dominated main episode that is found in a substantial minority, ∼10% of GRBs. A correct identification of the emission phase is thus required to infer the properties of the flow and of the immediate environment around GRB progenitors.