The origin of magnetic fields that permeate the blast waves of gamma-ray bursts ( GRBs ) is a long-standing problem . The present paper argues that in four GRBs revealing extended emission at > 100 { MeV } , with follow-up in the radio , optical and X-ray domains at later times , this magnetization can be described as the partial decay of the micro-turbulence that is generated in the shock precursor . Assuming that the bulk of the extended emission > 100 MeV can be interpreted as synchrotron emission of shock-accelerated electrons , we model the multi-wavelength light curves of GRB 090902B , GRB 090323 , GRB 090328 and GRB 110731A , using a simplified then a full synchrotron calculation with power-law-decaying micro-turbulence \epsilon _ { B } \propto t ^ { \alpha _ { t } } ( t denotes the time since injection through the shock , in the comoving blast frame ) . We find that these models point to a consistent value of the decay exponent -0.5 \lesssim \alpha _ { t } \lesssim -0.4 .