Learning analytics dashboards (LADs) simplify complex learner data into accessible visualisations, providing actionable insights for educators and students. However, their educational effectiveness has not always matched the sophistication of the technology behind them. Explanatory and interactive LADs, enhanced by generative AI (GenAI) chatbots, hold promise by enabling dynamic, dialogue-based interactions with data visualisations and offering personalised feedback through text. Yet, the effectiveness of these tools may be limited by learners' varying levels of GenAI literacy, a factor that remains underexplored in current research. This study investigates the role of GenAI literacy in learner interactions with conventional (reactive) versus scaffolding (proactive) chatbot-assisted LADs. Through a comparative analysis of 81 participants, we examine how GenAI literacy is associated with learners' ability to interpret complex visualisations and their cognitive processes during interactions with chatbot-assisted LADs. Results show that while both chatbots significantly improved learner comprehension, those with higher GenAI literacy benefited the most, particularly with conventional chatbots, demonstrating diverse prompting strategies. Findings highlight the importance of considering learners' GenAI literacy when integrating GenAI chatbots in LADs and educational technologies. Incorporating scaffolding techniques within GenAI chatbots can be an effective strategy, offering a more guided experience that reduces reliance on learners' GenAI literacy.