  Resonant scattering of weak coherent laser pulses on a single two-level
system (TLS) realized in a semiconductor quantum dot is investigated with
respect to a time delay between incoming and scattered light. This type of time
delay was predicted by Wigner in 1955 for purely coherent scattering and was
confirmed for an atomic system in 2013 [R. Bourgain et al., Opt. Lett. 38, 1963
(2013)]. In the presence of electron-phonon interaction we observe deviations
from Wigner's theory related to incoherent and strongly non-Markovian
scattering processes which are hard to quantify via a detuning-independent pure
dephasing time. We observe detuning-dependent Wigner delays of up to 530\,ps in
our experiments which are supported quantitatively by microscopic theory
allowing for pure dephasing times of up to 950\,ps.
