  The highly luminous and variable prompt emission in Gamma-Ray Bursts (GRBs)
arises in an ultra-relativistic outflow. The exact underlying radiative
mechanism shaping its non-thermal spectrum is still uncertain, making it hard
to determine the outflow's bulk Lorentz factor $\Gamma$. GRBs with spectral
cutoff due to pair production ($\gamma\gamma\to e^+e^-$) at energies
$E_c\gtrsim10\;$MeV are extremely useful for inferring $\Gamma$. We find that
when the emission region has a high enough compactness, then as it becomes
optically thick to scattering, Compton downscattering by non-relativistic
$e^\pm$-pairs can shift the spectral cutoff energy well below the
self-annihilation threshold, $E_{\rm sa}=\Gamma m_ec^2/(1+z)$. We treat this
effect numerically and show that $\Gamma$ obtained assuming $E_c=E_{\rm sa}$
can under-predict its true value by as much as an order of magnitude.
