This paper addresses a challenging interactive task learning scenario we call rearrangement under unawareness: an agent must manipulate a rigid-body environment without knowing a key concept necessary for solving the task and must learn about it during deployment. For example, the user may ask to "put the two granny smith apples inside the basket", but the agent cannot correctly identify which objects in the environment are "granny smith" as the agent has not been exposed to such a concept before. We introduce SECURE, an interactive task learning policy designed to tackle such scenarios. The unique feature of SECURE is its ability to enable agents to engage in semantic analysis when processing embodied conversations and making decisions. Through embodied conversation, a SECURE agent adjusts its deficient domain model by engaging in dialogue to identify and learn about previously unforeseen possibilities. The SECURE agent learns from the user's embodied corrective feedback when mistakes are made and strategically engages in dialogue to uncover useful information about novel concepts relevant to the task. These capabilities enable the SECURE agent to generalize to new tasks with the acquired knowledge. We demonstrate in the simulated Blocksworld and the real-world apple manipulation environments that the SECURE agent, which solves such rearrangements under unawareness, is more data-efficient than agents that do not engage in embodied conversation or semantic analysis.