  \textit{Ab initio} quantum Monte Carlo (QMC) methods in principle allow for
the calculation of exact properties of correlated many-electron systems, but
are in general limited to the simulation of a finite number of electrons $N$ in
periodic boundary conditions. Therefore, an accurate theory of finite-size
effects is indispensable to bridge the gap to realistic applications in the
thermodynamic limit. In this work, we revisit the uniform electron gas (UEG) at
finite temperature as it is relevant to contemporary research e.g. in the field
of warm dense matter. In particular, we present a new scheme to eliminate
finite-size effects both in the static structure factor $S(q)$ and in the
interaction energy $v$, which is based on the density response formalism. We
demonstrate that this method often allows to obtain $v$ in the TDL within a
relative accuracy of $\sim0.2\%$ from as few as $N=4$ electrons without any
empirical choices or knowledge of results for other values of $N$. Finally, we
evaluate the applicability of our method upon increasing the density parameter
$r_s$ and decreasing the temperature $T$.
