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Tables provide valuable knowledge that can be used to verify textual statements. While a number of works have considered table-based fact verification, direct alignments of tabular data with tokens in textual statements are rarely available. Moreover, training a generalized fact verification model requires abundant labeled training data. In this paper, we propose a novel system to address these problems. Inspired by counterfactual causality, our system identifies token-level salience in the statement with probing-based salience estimation. Salience estimation allows enhanced learning of fact verification from two perspectives. From one perspective, our system conducts masked salient token prediction to enhance the model for alignment and reasoning between the table and the statement. From the other perspective, our system applies salience-aware data augmentation to generate a more diverse set of training instances by replacing non-salient terms. Experimental results on TabFact show the effective improvement by the proposed salience-aware learning techniques, leading to the new SOTA performance on the benchmark.