Graph-based Semi-Supervised Learning (GSSL) is a practical solution to learn from a limited amount of labelled data together with a vast amount of unlabelled data. However, due to their reliance on the known labels to infer the unknown labels, these algorithms are sensitive to data quality. It is therefore essential to study the potential threats related to the labelled data, more specifically, label poisoning. In this paper, we propose a novel data poisoning method which efficiently approximates the result of label inference to identify the inputs which, if poisoned, would produce the highest number of incorrectly inferred labels. We extensively evaluate our approach on three classification problems under 24 different experimental settings each. Compared to the state of the art, our influence-driven attack produces an average increase of error rate 50% higher, while being faster by multiple orders of magnitude. Moreover, our method can inform engineers of inputs that deserve investigation (relabelling them) before training the learning model. We show that relabelling one-third of the poisoned inputs (selected based on their influence) reduces the poisoning effect by 50%.