To realize spin wave logic gates, programmable phase inverters are essential. We image using phase-resolved Brillouin light scattering microscopy propagating spin waves in a one-dimensional magnonic crystal consisting of dipolarly coupled magnetic nanostripes. We demonstrate phase shifts upon a single nanostripe of opposed magnetization. Using micromagnetic simulations, we model our experimental finding in a wide parameter space of biasfields and wave vectors. We find that low-loss phase inversion is achieved, when the internal field of the oppositely magnetized nanostripe is tuned such that the latter supports a resonant standing spin wave mode with an odd quantization number at the given frequency. Our results are key for the realization of phase inverters with optimized signal transmission.