Material science methods aim at developing efficient computational schemes for describing complex many-body effects and how they are revealed in experimentally measurable properties. Bethe-Salpeter equation in the self-consistent Hartree-Fock basis is often used for this purpose, and in this paper we employ the real-frequency diagrammatic Monte Carlo framework for solving the ladder-type Bethe-Salpeter equation for the 3-point vertex function (and, ultimately, for the system's polarization) to study the effect of electron-hole Coulomb scattering on Landau damping in the homogeneous electron gas. We establish how this damping mechanism depends on the Coulomb parameter $r_s$ and changes with temperature between the correlated liquid and thermal gas regimes. In a broader context of dielectric response in metals, we also present the full polarization and the typical dependence of the exchange-correlation kernel on frequency at finite momentum and temperature within the same computational framework.

5 pages and 4 figures