This paper addresses a challenging interactive task learning scenario we call rearrangement under unawareness: to manipulate a rigid-body environment in a context where the robot is unaware of a concept that's key to solving the instructed task. We propose SECURE, an interactive task learning framework designed to solve such problems by fixing a deficient domain model using embodied conversation. Through dialogue, the robot discovers and then learns to exploit unforeseen possibilities. Using SECURE, the robot not only learns from the user's corrective feedback when it makes a mistake, but it also learns to make strategic dialogue decisions for revealing useful evidence about novel concepts for solving the instructed task. Together, these abilities allow the robot to generalise to subsequent tasks using newly acquired knowledge. We demonstrate that a robot that is semantics-aware -- that is, it exploits the logical consequences of both sentence and discourse semantics in the learning and inference process -- learns to solve rearrangement under unawareness more effectively than a robot that lacks such capabilities.