Transformer-based methods have exhibited significant generalization ability when prompted with target-domain demonstrations or example solutions during inference. Although demonstrations, as a way of task specification, can capture rich information that may be hard to specify by language, it remains unclear what information is extracted from the demonstrations to help generalization. Moreover, assuming access to demonstrations of an unseen task is impractical or unreasonable in many real-world scenarios, especially in robotics applications. These questions motivate us to explore what the minimally sufficient prompt could be to elicit the same level of generalization ability as the demonstrations. We study this problem in the contextural RL setting which allows for quantitative measurement of generalization and is commonly adopted by meta-RL and multi-task RL benchmarks. In this setting, the training and test Markov Decision Processes (MDPs) only differ in certain properties, which we refer to as task parameters. We show that conditioning a decision transformer on these task parameters alone can enable zero-shot generalization on par with or better than its demonstration-conditioned counterpart. This suggests that task parameters are essential for the generalization and DT models are trying to recover it from the demonstration prompt. To extract the remaining generalizable information from the supervision, we introduce an additional learnable prompt which is demonstrated to further boost zero-shot generalization across a range of robotic control, manipulation, and navigation benchmark tasks.