Generative artificial intelligence (GenAI) tools are gaining popularity in academia, despite concerns about hallucinations and misinformation, which raises questions about their reliability in educational contexts. A key gap lies in the lack of interventions that encourage critical evaluation of GenAI content. Our study addresses this gap by introducing Nudgr, a digital nudging tool designed to promote fact-checking behaviours when using GenAI tools. Nudgr is implemented as a popover alert within GenAI interfaces. It delivers tailored nudge messages, context-relevant keyword suggestions, and one-click verification buttons to direct learners to verify the accuracy of GenAI responses. We evaluated Nudgr with 13 university students, comprising undergraduates and postgraduates across different disciplines. Overall, Nudgr shows promise as a tool that promotes learners’ engagement to verify AI-generated content critically. Its design fosters trust, reduces cognitive effort, and enables faster and more user-friendly fact-checking. It offers a practical response to the challenges posed by misinformation in GenAI use.