While the disruptive impact of the COVID-19 pandemic continues to unfold around the world, one of its most immediate effects -- beyond significant loss of life and livelihood -- has been the exposure of existing weaknesses in various sectors and systems. This is especially evident in higher education, with its growing overreliance on the (hyper)mobile student body. In this paper we explore critically the challenges and possibilities behind the options of "reframing" and "hospicing" current understandings of student mobility, particularly with respect to the simultaneously romanticized and commodified development of intercultural (communicative) competence. We treat reframing and hospicing as concurrent, co-existing approaches and spaces in which we may dwell as we rethink what it means to engage meaningfully and equitably with difference at both global and local levels. We also explore how "hospicing" may help us to disinvest ourselves from the promises of mobility, letting go of our attachment to it, not simply because of its current impossibility, but rather because of its many ideological and ethical problems. We conclude with a set of critical, reflective questions intended as provocations that may stimulate ongoing dialogue in our shared journeys of knowing, being and relating to ourselves and the Other in the world.