Contestability is a highly desirable property for human-centric AI, ensuring that the outcomes of an AI system can be challenged, and possibly changed, when interacting with humans and/or other AI systems. In this paper we study contestability of argumentative claims obtained from Assumption-Based Argumentation (ABA) frameworks, a unifying formalism for various non-monotonic reasoning methods that can be used for explainable AI systems. Specifically, we focus on ABA frameworks that are learnt with ABA Learning, a recent approach to symbolic learning from positive and negative examples, given a background knowledge . We formally define a notion of contestation when desirable claims are rejected or undesirable claims are accepted in learnt ABA frameworks. We also show that ABA Learning can be adapted to redress issues raised by contestation so that the desirable claims are accepted and the undesirable claims are rejected. This is naturally achieved by extending the learnt ABA framework without restarting from scratch, and instead preserving as much as possible thereof by considering some of its rules defeasible. We conduct several experiments with a variety of tabular datasets to demonstrate the computational advantages of our contestable ABA Learning in comparison with re-learning from scratch.