As deep language models (DLMs) are increasingly deployed in high-stakes domains such as healthcare, understanding their decision rationale becomes paramount for ensuring trust, safety, and accountability. However, achieving this vital level of interpretability is particularly challenging when these DLMs operate as black-box systems (e.g., via APIs), where access to internal model states (e.g., parameters, gradients) is restricted. Despite numerous efforts, existing explanation methods often fail to concurrently satisfy three key desiderata: (i) inference-time efficiency, (ii) black-box compatibility without inducing out-of-distribution behavior, and (iii) comprehensible explanations grounded in the input's linguistic structure. To address these challenges, we propose a method that explains predictions of DLMs by selecting a small, informative subset of input words. We formulate this as an amortized optimization problem, enabling efficient one-shot inference without the need for input-specific search. Our selection policy is trained via REINFORCE-style policy gradients, allowing discrete word selection in a fully gradient-free setting. To enhance interpretability and align with human linguistic intuition, we integrate graph-structured knowledge into this selection process, fostering linguistically coherent subsets that result in explanations both highly informative and cognitively meaningful to end-users. We evaluated our method on diverse DLM architectures and multiple real-world datasets. It consistently identifies word subsets with enhanced discriminative power and stronger alignment with linguistically salient cues, outperforming both conventional black-box compatible methods and gradient-based approaches that are given oracle access to the black-box model's gradients for a more challenging benchmark. Our code is available at here.