  QCD kinetic theory simulations are a prominent tool for studying the
nonequilibrium initial stages in heavy-ion collisions. Despite their success,
all implementations rely on approximations of the hard thermal loop (HTL)
screened matrix elements in the collision terms. In this paper, we present our
results for different isotropic screening prescriptions in the elastic
collision term for gluons. In particular, we go beyond the simple Debye-like
screening form that is used in all current implementations and apply the
isotropic HTL matrix element instead. For isotropic systems, the evolution is
nearly unchanged, but when studying the equilibration process in a Bjorken
expanding plasma, we find qualitative and quantitative differences in a range
of moments of the distribution function, such as a decrease in the maximum
pressure anisotropy by up to 50%. In contrast, we find no significant
qualitative impact on the jet quenching parameter or on the late-time
hydrodynamization dynamics of anisotropic plasmas but observe systematically
smaller values of $\eta/s$ by about 10% that coincide with perturbative
calculations at small couplings. Our study reveals that the choice of the
screening prescription can lead to large corrections at early times, but is
less important close to equilibrium.
