  We investigate, both analytically and numerically, the scattering of
one-dimensional quantum droplets by a P\"{o}schl-Teller reflectionless
potential well, confirming that there is a sharp transition between full
reflection and full transmission at a certain critical incident speed for both
small droplets and large flat-top droplets. We observe sharp differences
between small quantum droplet scattering and large quantum droplet scattering.
The scattering of small quantum droplets is similar to that of solitons, where
a spatially symmetric trapped mode is formed at the critical speed, whereas for
large quantum droplets a spatially asymmetric trapped mode is formed.
Additionally, a nonmonotonous dependence of the critical speed on the atom
number is identified$:$ on the small-droplet side, the critical speed increases
with the atom number, while in the flat-top regime, the critical speed
decreases with increasing the atom number. Strikingly, the scattering excites
internal modes below the particle-emission threshold, preventing the quantum
droplets from emitting radiation upon interaction with the potential. Analysis
of the small-amplitude excitation spectrum shows that as the number of
particles increases, it becomes increasingly difficult to emit particles
outside the droplet during scattering, while radiation from solitons cannot be
completely avoided. Finally, we study the collision of two quantum droplets at
the reflectionless potential, revealing the role of the $\pi$-phase difference
``generator'' played by the reflectionless potential.
