  We study the geometric phase of a two-level system under the presence of a
structured environment, particularly analysing its correction with the ohmicity
parameter $s$ and the onset of non-Markovianity. We firstly examine the system
coupled to a set of harmonic oscillators and studied the decoherence factor as
function of the environment's ohmicity parameter. Secondly, we propose the
two-level system coupled to a non-equilibrium environment, and show that these
environments display non-Markovian effects for all values of the ohmicity
parameter. The geometric phase of the two-level system is therefore computed
under the presence of both types of environment. The correction to the unitary
geometric phase is analysed in both, Markovian and non-Markovian regimes. Under
Markovian environments, the correction induced on the system's phase is mainly
ruled by the coupling constant between the system and the environment, while in
the non-Markovian regime, memory effects seem to trigger a significant
correction to the unitary geometric phase. The result is significant to the
quantum information processing based on the geometric phase in quantum open
systems
