Conversational assistive robots can aid people, especially those with cognitive impairments, to accomplish various tasks such as cooking meals, performing exercises, or operating machines. However, to interact with people effectively, robots must recognize human plans and goals from noisy observations of human actions, even when the user acts sub-optimally. Previous works on Plan and Goal Recognition (PGR) as planning have used hierarchical task networks (HTN) to model the actor/human. However, these techniques are insufficient as they do not have user engagement via natural modes of interaction such as language. Moreover, they have no mechanisms to let users, especially those with cognitive impairments, know of a deviation from their original plan or about any sub-optimal actions taken towards their goal. We propose a novel framework for plan and goal recognition in partially observable domains -- Dialogue for Goal Recognition (D4GR) enabling a robot to rectify its belief in human progress by asking clarification questions about noisy sensor data and sub-optimal human actions. We evaluate the performance of D4GR over two simulated domains -- kitchen and blocks domain. With language feedback and the world state information in a hierarchical task model, we show that D4GR framework for the highest sensor noise performs 1% better than HTN in goal accuracy in both domains. For plan accuracy, D4GR outperforms by 4% in the kitchen domain and 2% in the blocks domain in comparison to HTN. The ALWAYS-ASK oracle outperforms our policy by 3% in goal recognition and 7%in plan recognition. D4GR does so by asking 68% fewer questions than an oracle baseline. We also demonstrate a real-world robot scenario in the kitchen domain, validating the improved plan and goal recognition of D4GR in a realistic setting.