In this article, we study the nonlinear dynamics of a laser subjected to frequency shifted optical reinjection coming back from a vibrating target. More specifically, we study the nonlinear dynamical coupling between the carrier and the vibration signal. The present work shows how the nonlinear amplification of the vibration spectrum is related to the strength of the carrier and how it must be compensated to obtain accurate (i.e., without bias) vibration measurements. The theoretical predictions, confirmed by numerical simulations, are in good agreement with the experimental data. The main motivation of this study is the understanding of the nonlinear response of a laser optical feedback imaging sensor for quantitative phase measurements of small vibrations in the case of strong optical feedback.