Summary: This paper is concerned with the problem of modifying the edge lengths of a weighted extended star network with \(n\) vertices by integer amounts at the minimum total cost subject to be given modification bounds so that a set of \(p\) prespecified vertices becomes an undesirable \(p\)-median location on the perturbed network. We call this problem as the integer inverse undesirable \(p\)-median location model. Exact combinatorial algorithms with \(\mathcal{O}\left(p^2 n \log n\right)\) and \(\mathcal{O} \left(p^2(n \log n+ n \log \eta_{\max})\right)\) running times are proposed for solving the problem under the weighted rectilinear and weighted Chebyshev norms, respectively. Furthermore, it is shown that the problem under the weighted sum-type Hamming distance with uniform modification bounds can be solved in \(\mathcal{O} (p^2n \log n)\) time.