The Granger test is one of the best known techniques to detect causality relationships among time series, and has been used uncountable times in science and engineering. The quality of its results strongly depends on the quality of the underlying data, and different approaches have been proposed to reduce the impact of, for instance, observational noise or irregular sampling. Less attention has nevertheless been devoted to situations in which the analysed time series are irregularly polluted with missing and extreme values. In this contribution I tackle this problem by comparing four different data pre-processing strategies and evaluating their performance with synthetic time series, both in dyadic tests and functional network contexts. I further apply these strategies to a real-world problem, involving inferring the structure behind the propagation of delays in an air transport system. Finally, some guidelines are provided on when and how these strategies ought to be used.