  The intergalactic magnetic field (IGMF) present in the voids of large-scale
structures is considered to be the weakest magnetic field in the Universe.
Gamma-ray observations of blazars in the GeV-TeV domain have led to lower
limits on the IGMF strength based on the search for delayed or extended
emission. Nevertheless, these results have been obtained with strong
assumptions placed on the unknown source properties. The recent discovery of
TeV radiation from gamma-ray bursts (GRBs) has paved the way for IGMF studies
with these bright transients. Among the current TeV-detected GRBs, GRB 190114C,
located at a redshift of $z = 0.42$, is the best sampled. Therefore, it can be
considered to be representative of the properties of GRBs in the VHE domain. In
addition, GRB 221009A ($z = 0.151$) is the brightest event ever detected. We
present a phenomenological model based on the intrinsic properties of GRB
190114C and GRB 221009A to predict the delayed emission component (pair-echo)
in the GeV-TeV band. We investigate the detectability of this component from
low-redshift ($z \leq 1$) GRBs for three values of IGMF strength ($10^{-19}$ G,
$10^{-18}$ G and $10^{-17}$ G), different observational times ($3$ hrs, $6$
hrs, and $9$ hrs) and source intrinsic properties. We find that for current and
future generation $\gamma$-ray instruments, extending the observation for at
least 3 hours after the GRB detection is a viable strategy for probing the
IGMF. We also confirm that GeV-TeV observations of GRBs can probe IGMF
strengths on the order of $10^{-17} -10^{-19}$ G, representing a competitive
alternative to the current studies performed with active galactic nuclei
(AGNs).
