  Gravitational lensing of a gamma ray burst (GRB) by a single point mass will
produce a second, delayed signal. Several authors have discussed using
microlensed GRBs to probe a possible cosmological population of compact
objects. We analyse a closely related phenomenon; the effect of microlensing by
low to medium optical depth in compact objects on the averaged observed
light-curve of a sample of GRBs. We discuss the cumulative measured flux as a
function of time resulting from delays due to microlensing by cosmological
compact objects. The time-scale and curvature of this function describe unique
values for the compact object mass and optical depth. For GRBs with durations
larger than the detector resolution, limits could be placed on the mass and
optical depth of cosmological compact objects. The method does not rely on the
separation of lensed bursts from those which are spatially coincident.
