In this paper we analyze security of robust data-hiding in channels with geometrical transformations. We categorize possible decoding strategies for channels with geometrical transformations within the information-theoretic framework for geometrically-robust datahiding. Furthermore, considering template-based and redundantbased design of geometrically robust data-hiding systems, we provide the analysis of general attacking strategies and particular attacking scenarios for each group of structured codebooks. Finally, reversibility of data-hiding and effect of security leakages on system performance are investigated.