While de-identification models can help conceal the identity of the individuals mentioned in a document, they fail to address linkage risks, defined as the potential to map the de-identified text back to its source. One straightforward way to perform such linkages is to extract phrases from the de-identified document and check their presence in the original dataset. This paper presents a method to counter search-based linkage attacks while preserving the semantic integrity of the text. The method proceeds in two steps. We first construct an inverted index of the N-grams occurring in the text collection, making it possible to efficiently determine which N-grams appear in fewer than $k$ documents, either alone or in combination with other N-grams. An LLM-based rewriter is then iteratively queried to reformulate those spans until linkage is no longer possible. Experimental results on two datasets (court cases and Wikipedia biographies) show that the rewriting method can effectively prevent search-based linkages while remaining faithful to the original content. However, we also highlight that linkages remain feasible with the help of more advanced, semantics-oriented approaches.