The dissolution of complexes formed by a linear polyelectrolyte and oppositely charged macroions by addition of salt has been examined by employing a simple model with focus on the electrostatic interactions and solved by Monte Carlo simulations. In the absence of salt an overcharged complex appears. Upon addition of salt, the number of complexed macroions is continuously decreasing, the effect being similar for flexible and stiff polyelectrolytes. Regarding the flexible polyelectrolyte, the number of polyelectrolyte-macroion contacts is reduced, whereas it remains nearly constant for the stiff polyelectrolyte as the salt content is increased. A screened Coulomb potential of the Debye-Hückel type, in which the small ions are only indirectly described, displays a good representation of the system.