The prevalence of mobile devices and Location-Based Services (LBS) necessitate the study of Location Privacy-Preserving Mechanisms (LPPM). However, LPPMs reduce the utility of LBS due to the noise they add to users' locations. Here, we consider the remapping technique, which presumes the adversary has a perfect statistical model for the user location. We consider this assumption and show that under practical assumptions on the adversary's knowledge, the remapping technique leaks privacy not only about the true location data, but also about the statistical model. Finally, we introduce a novel solution called "Randomized Remapping" as a countermeasure.