Generative artificial intelligence (GenAI) is increasingly integrated into higher education, where it supports writing, feedback, problem solving, and research-related tasks while also raising concerns about cognitive offloading and learner dependence. This scoping review mapped the literature on the relationships among GenAI, cognitive offloading, and learner agency in higher education. Peer-reviewed English-language studies were reviewed to examine how learner agency has been conceptualized, how GenAI may both enhance and erode agency, which mechanisms link GenAI use to educational outcomes, and which pedagogical conditions shape these effects. The review shows that learner agency is conceptualized as a multidimensional construct involving self-regulation, reflective judgement, intentionality, and responsible action. Across the literature, GenAI operates through a dual-pathway structure: one pathway may enhance learner agency by strengthening self-regulated learning, self-efficacy, feedback literacy, and reflective engagement, whereas the other may erode learner agency through cognitive offloading, overreliance, dependence, uncritical uptake, and weakened judgement. Overall, the findings suggest that the educational value of GenAI depends less on the technology itself than on how it is pedagogically embedded, with augmentation-oriented and scaffolded use being more supportive of learner agency than replacement-oriented use.