In road traffic, mental overload often leads to a failure to notice new and distinctive stimuli. Such phenomenon is known as 'inattentional blindness'. Safe and efficient interaction between automated vehicles (AVs) and pedestrians is expected to rely heavily on external human-machine interfaces (eHMIs), a tool AVs are equipped with to communicate their intentions to pedestrians. This study seeks to explore the phenomenon of 'inattentional blindness' in the context of pedestrian-AV interactions. Specifically, the aim is to understand the effects of a warning eHMI on pedestrians' crossing decisions when they are engaged in a secondary task. In an experiment study with videos of pedestrian crossing scenarios filmed from the perspective of the crossing pedestrian, participants had to decide the latest point at which they would be willing to cross the road in front of an AV with an eHMI vs. an AV without an eHMI. Participants were also asked to predict the future behavior of the AV. 125 female and 9 male participants aged between 18 and 25 completed the experiment and a follow-up questionnaire. It was found that the presence of a warning eHMI on AVs contributes to a clearer understanding of pedestrians' inferences about the intention of AVs and helps deter late and dangerous crossing decisions made by pedestrians. However, the eHMI fail to help pedestrians avoid such decisions when they face a high mental workload induced by secondary task engagement.