Generative AI (GenAI)-related misinformation has emerged as a significant concern for higher education learners, yet research on the factors that affect fact-checking of GenAI remains limited. Drawing on the lens of heuristic-systematic processing within dual process theory, this paper addresses the current gap by examining how GenAI users process information and respond to potential misinformation generated by such tools during learning. Two information processing mechanisms, heuristic (prompt, shortcut-based, convenient thinking) and systematic (in-depth, critical, dedicated thinking), were examined. This study proposed a conceptual model with the intention to fact-check GenAI responses, positing that digital literacy, information processing mechanisms, and information self-efficacy are essential components. To test this model, path analysis was conducted on self-reported survey data collected from 668 higher education learners. Findings showed that digital literacy in GenAI usage positively influences the intention to fact-check GenAI information, both directly and indirectly through information self-efficacy and user heuristics. The influence of digital literacy on the intention to fact-check GenAI Information is also sequentially mediated by systematic processing, which, in turn, influences information self-efficacy. Theoretically, these findings extend the human-AI interaction literature by applying dual process theory to deepen our understanding of information processing in AI-mediated learning. The results also contribute to policy and practice, especially by underscoring the role of digital literacy in GenAI to foster fact-checking of GenAI outputs.