Localization plays an increasingly pivotal role in 5G/6G systems, enabling various applications. This paper focuses on the privacy concerns associated with delay-based localization, where unauthorized base stations attempt to infer the location of the end user. We propose a method to disrupt localization at unauthorized nodes by injecting artificial components into the pilot signal, exploiting model mismatches inherent in these nodes. Specifically, we investigate the effectiveness of two techniques, namely artificial multipath (AM) and artificial noise (AN), in mitigating location leakage. By leveraging the misspecified Cram\'er-Rao bound framework, we evaluate the impact of these techniques on unauthorized localization performance. Our results demonstrate that pilot manipulation significantly degrades the accuracy of unauthorized localization while minimally affecting legitimate localization. Moreover, we find that the superiority of AM over AN varies depending on the specific scenario.