We describe the Markovian dynamics of the Gaussian interferometric power of two-mode Gaussian states, for a system composed of two bosonic modes, each one interacting with its squeezed thermal bath, in the framework of the theory of open systems based on completely positive quantum dynamical semigroups. The time evolution of the interferometric power is described in terms of the covariance matrix for Gaussian initial states. The behaviour of the Gaussian interferometric power depends on the initial state of the subsystem (squeezing parameter and thermal photon num-bers) and on the parameters characterizing the squeezed thermal reservoirs (tempera-tures, dissipation coefficient, squeezed parameters of the baths and squeezing angle). We show that, independently of the initial state, the Gaussian interferometric power is monotonically decreasing in time, and in the limit of large times it asymptotically decreases to a zero value.