We present a physical mechanism that explains the recent observations of incoherent writing and erasure of Cavity Solitons in a semiconductor optical amplifier [S. Barbay et al, Opt. Lett. 31, 1504-1506 (2006)]. This mechanism allows to understand the main observations of the experiment. In particular it perfectly explains why writing and erasure are possible as a result of a local perturbation in the carrier density, and why a delay is observed along with the writing process. Numerical simulations in 1D are performed and show very good qualitative agreement with the experimental observations.