In planar piecewise linear differential systems, we analyse the cyclicity in breaking the heteroclinic connection of hyperbolic saddles bounding a period annulus. For certain parameter values, the saddles become resonant. When the system is perturbed generically within the framework of piecewise linear systems, the first-order number of limit cycles that persist near the connection differs depending on the saddles have hyperbolicity ratio one (strongly resonant case), or not. In particular, fewer limit cycles persist in the resonant case. To establish this result we analyse the structure of the displacement map and we show that it depends on whether there is a strong resonance in the saddle or not.