Text embedding models have significantly contributed to advancements in natural language processing by adeptly capturing semantic properties of textual data. However, the ability of these models to generalize across a wide range of syntactic contexts remains under-explored. In this paper, we first develop an evaluation set, named SR, to scrutinize the capability for syntax understanding of text embedding models from two crucial syntactic aspects: Structural heuristics, and Relational understanding among concepts, as revealed by the performance gaps in previous studies. Our findings reveal that existing text embedding models have not sufficiently addressed these syntactic understanding challenges, and such ineffectiveness becomes even more apparent when evaluated against existing benchmark datasets. Furthermore, we conduct rigorous analysis to unearth factors that lead to such limitations and examine why previous evaluations fail to detect such ineffectiveness. Lastly, we propose strategies to augment the generalization ability of text embedding models in diverse syntactic scenarios. This study serves to highlight the hurdles associated with syntactic generalization and provides pragmatic guidance for boosting model performance across varied syntactic contexts.