We have measured directly the Andreev scattering of a controllable beam of quasiparticle excitations by a localized tangle of quantum vortices in superfluid He-3-B at low temperatures. We present a microscopic description of the Andreev scattering from a vortex line allowing us to estimate the vortex separation scale in a dilute tangle of vortices, providing a better comparison of the observed decay time of the turbulence with recent numerical simulations. The experiments also suggest that below 200 muK we reach the low temperature limit for turbulent dynamics.