The staggered model is a recent, very general variant of discrete-time quantum walks which, avoiding the use of a coin to direct the walker evolution, explores the underlying graph structure to build an evolution operator based on local unitaries induced by adjacent vertices. Optimising their implementation to increase resilience to decoherence phenomena motivates their analysis with the ZX-calculus. The whole optimisation can be seen as a graph reconfiguration process along which the original circuit is rewrote, significantly reducing the number of (expensive) gates used. The exercise identified an underlying pattern leading to an alternative, potentially more efficient evolution operator.