Internationalization at a distance (IaD) has been loosely defined as distance education across borders or the international mobility of knowledge without human mobility. It is largely celebrated, for example, for its potential to improve global education access and mitigate environmental harm. However, this depoliticized positioning risks overlooking IaD's relationship to uneven human mobility flows structured by global inequities. In response, this paper calls for a critical IaD research agenda, starting by drawing attention to the mobility politics of IaD at the postsecondary level. First, it proposes a more nuanced conceptualization of IaD rooted in insights from critical border studies, described here as "bordered distance education." Second, it suggests the use of two theorizations of capital--citizenship and motility--as avenues to deepen future analysis of not only IaD but also international student mobility more generally. Third, to demonstrate the application of these suggestions, it presents a critical policy discourse analysis of international student mobility policies during the COVID-19 pandemic era and its aftermath (2000-2024) in Canada. This case study shows how (1) distance education can be used as a bordering tool, and (2) governments can manipulate international student mobility policy to ensure IaD primarily serves immigration, as opposed to educational, needs.