  We investigate the delayed, secondary GeV-TeV emission of gamma-ray bursts
and its potential to probe the nature of intergalactic magnetic fields.
Geometrical effects are properly taken into account for the time delay between
primary high energy photons and secondary inverse Compton photons from
electron-positron pairs, which are produced in $\gamma$-$\gamma$ interactions
with background radiation fields and deflected by intervening magnetic fields.
The time-dependent spectra of the delayed emission are evaluated for a wide
range of magnetic field strengths and redshifts. The typical flux and delay
time of secondary photons from bursts at $z \sim 1$ are respectively $\sim
10^{-8}$ GeV cm$^{-2}$ s$^{-1}$ and $\sim 10^4$ s if the field strengths are
$\sim 10^{-18}$ G, as might be the case in intergalactic void regions. We find
crucial differences between the cases of coherent and tangled magnetic fields,
as well as dependences on the field coherence length.
