As a widely explored multi-modal task, Temporal Sentence Grounding in videos (TSG) endeavors to retrieve a specific video segment matched with a given query text from a video. The traditional paradigm for TSG generally assumes that relevant segments always exist within a given video. However, this assumption is restrictive and unrealistic in real-world applications where the existence of a query-related segment is uncertain, easily resulting in erroneous grounding. Motivated by the research gap and practical application, this paper introduces a new task, named Temporal Sentence Grounding with Relevance Feedback (TSG-RF) in videos, which accommodates the possibility that a video may or may not include a segment related to the query. This task entails localizing precise video segments that semantically align with the query text when such content is present, while delivering definitive feedback on the non-existence of related segments when absent. Moreover, we propose a novel Relation-aware Temporal Sentence Grounding (RaTSG) network for addressing this challenging task. This network first reformulates the TSG-RF task as a foreground-background detection problem by investigating whether the query-related semantics exist in both frame and video levels. Then, a multi-granularity relevance discriminator is exploited to produce precise video-query relevance feedback and a relation-aware segment grounding module is employed to selectively conduct the grounding process, dynamically adapting to the presence or absence of query-related segments in videos. To validate our RaTSG network, we reconstruct two popular TSG datasets, establishing a rigorous benchmark for TSG-RF. Experimental results demonstrate the effectiveness of our proposed RaTSG for the TSG-RF task. Our source code is available at https://github.com/HuiGuanLab/RaTSG.