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Explanations are crucial parts of deep neural network (DNN) classifiers. In high stakes applications, faithful and robust explanations are important to understand and gain trust in DNN classifiers. However, recent work has shown that state-of-the-art attribution methods in text classifiers are susceptible to imperceptible adversarial perturbations that alter explanations significantly while maintaining the correct prediction outcome. If undetected, this can critically mislead the users of DNNs. Thus, it is crucial to understand the influence of such adversarial perturbations on the networks' explanations and their perceptibility. In this work, we establish a novel definition of attribution robustness (AR) in text classification, based on Lipschitz continuity. Crucially, it reflects both attribution change induced by adversarial input alterations and perceptibility of such alterations. Moreover, we introduce a wide set of text similarity measures to effectively capture locality between two text samples and imperceptibility of adversarial perturbations in text. We then propose our novel TransformerExplanationAttack (TEA), a strong adversary that provides a tight estimation for attribution robustness in text classification. TEA uses state-of-the-art language models to extract word substitutions that result in fluent, contextual adversarial samples. Finally, with experiments on several text classification architectures, we show that TEA consistently outperforms current state-of-the-art AR estimators, yielding perturbations that alter explanations to a greater extent while being more fluent and less perceptible.