In the challenging context of Knowledge Graph (KG) construction from text, traditional approaches often rely on Open Information Extraction (OpenIE) pipelines. However, they are prone to generating many incorrect triplets. While domain specific Named Entity Recognition (NER) is commonly used to enhance the results, it compromises the domain independence and misses crucial triplets. To address these limitations, we introduce G-T2KG, a novel pipeline for KG construction that aims to preserve the domain independence while reducing incorrect triplets, thus offering a cost-effective solution without the need for domain-specific adaptations. Our pipeline utilizes state-of-the-art OpenIE combined with both a noun phrase-based cleaning and a LLMs based validation. It is evaluated using gold standards in two distinct domains (i.e., computer science and music) that we have constructed in the context of this study. On computer science corpus, the experimental results demonstrate a higher recall as compared to state-of-the-art approaches, and a higher precision notably increased by the integration of LLMs. Experiments on the music corpus show good performance, underscoring the versatility and effectiveness of G-T2KG in domain-independent KG construction.