  The detection of TeV gamma-ray bursts (GRBs) brought new opportunities to
study the physics of particle acceleration at relativistic shocks. The H.E.S.S.
telescopes recently observed very-high-energy (VHE) emission from a nearby
low-luminosity GRB, GRB 190829A. Follow-up observations with, e.g., Swift-XRT,
revealed unusual flare activities at $\sim 10^3\rm~s$, which can be caused by a
long-lasting central engine. We show that the VHE emission during the H.E.S.S.
observation time is naturally produced in the external inverse-Compton (EIC)
scenario, where seed photons supplied by the flares or other late-time
dissipation are upscattered to VHE energies by the non-thermal electrons
accelerated at the external forward shock. Our calculations show that the EIC
flare nearly coincides with the late-prompt flare, but extends $\sim3-4$ times
longer than the duration of the late-prompt flare. The preferred kinetic energy
and initial Lorentz factor used in our model are $\sim 10^{52}\rm~erg$ and
$\sim 20$, respectively. Understanding the mechanisms of the VHE emission from
low-luminosity GRBs will help us constrain the properties of the outflow and
the central engine activities, as well as the particle acceleration mechanism.
