As text generation systems' outputs are increasingly anthropomorphic -- perceived as human-like -- scholars have also increasingly raised concerns about how such outputs can lead to harmful outcomes, such as users over-relying or developing emotional dependence on these systems. How to intervene on such system outputs to mitigate anthropomorphic behaviors and their attendant harmful outcomes, however, remains understudied. With this work, we aim to provide empirical and theoretical grounding for developing such interventions. To do so, we compile an inventory of interventions grounded both in prior literature and a crowdsourcing study where participants edited system outputs to make them less human-like. Drawing on this inventory, we also develop a conceptual framework to help characterize the landscape of possible interventions, articulate distinctions between different types of interventions, and provide a theoretical basis for evaluating the effectiveness of different interventions.