The forward-backward semiclassical dynamics (FBSD) methodology is used to obtain expressions for time correlation functions of a system (atom or molecule) in solution. We use information-guided noise reduction (IGNoR) [Makri, N. Chem. Phys. Lett. 2004, 400, 446] to minimize the statistical error associated with the Monte Carlo integration of oscillatory functions. This is possible by reformulating the correlation function in terms of an oscillatory solvent-dependent contribution whose integral can be obtained analytically and a slowly varying function obtained via a grid-based iterative evaluation of solute properties. Knowledge of the exact integral of the oscillatory function, combined with correlated statistics, leads to partial cancellation of the Monte Carlo error. Application on a one-dimensional solute-solvent model shows a substantial improvement of convergence in the IGNoR-enhanced FBSD correlation function for a fixed number of Monte Carlo samples. The reduction of statistical error achieved by using the IGNoR methodology becomes more significant as the number of solvent particles increases.