There is an increase in the proliferation of online hate commensurate with the rise in the usage of social media. In response, there is also a significant advancement in the creation of automated tools aimed at identifying harmful text content using approaches grounded in Natural Language Processing and Deep Learning. Although it is known that training Deep Learning models require a substantial amount of annotated data, recent line of work suggests that models trained on specific subsets of the data still retain performance comparable to the model that was trained on the full dataset. In this work, we show how we can leverage influence scores to estimate the importance of a data point while training a model and designing a pruning strategy applied to the case of sexism detection. We evaluate the model performance trained on data pruned with different pruning strategies on three out-of-domain datasets and find, that in accordance with other work a large fraction of instances can be removed without significant performance drop. However, we also discover that the strategies for pruning data, previously successful in Natural Language Inference tasks, do not readily apply to the detection of harmful content and instead amplify the already prevalent class imbalance even more, leading in the worst-case to a complete absence of the hateful class.