We re-examine the quantum τq and transport τt scattering lifetimes due to background impurities in two-dimensional systems. We show that the well-known logarithmic divergence in the quantum lifetime is due to the non-physical assumption of an infinitely thick heterostructure, and demonstrate that the existing non-divergent multiple scattering theory can lead to unphysical quantum scattering lifetimes in high quality heterostructures. We derive a non-divergent scattering lifetime for finite thickness structures, which can be used both with lowest order perturbation theory and the multiple scattering theory. We calculate the quantum and transport lifetimes for electrons in generic GaAsAlGaAs heterostructures, and find that the correct 'rule of thumb' to distinguish the dominant scattering mechanisms in GaAs heterostructures should be τt/τq 10 for background impurities and τt/τq 10 for remote impurities. Finally we present the first comparison of theoretical results for τq and τt with experimental data from a GaAs 2DEG in which only background impurity scattering is present. We obtain excellent agreement between the calculations and experimental data, and are able to extract the background impurity density in both the GaAs and AlGaAs regions.