Robots interacting with humans through natural language can unlock numerous applications such as Referring Grasp Synthesis (RGS). Given a text query, RGS determines a stable grasp pose to manipulate the referred object in the robot's workspace. RGS comprises two steps: visual grounding and grasp pose estimation. Recent studies leverage powerful Vision-Language Models (VLMs) for visually grounding free-flowing natural language in real-world robotic execution. However, comparisons in complex, cluttered environments with multiple instances of the same object are lacking. This paper introduces HiFi-CS, featuring hierarchical application of Featurewise Linear Modulation (FiLM) to fuse image and text embeddings, enhancing visual grounding for complex attribute rich text queries encountered in robotic grasping. Visual grounding associates an object in 2D/3D space with natural language input and is studied in two scenarios: Closed and Open Vocabulary. HiFi-CS features a lightweight decoder combined with a frozen VLM and outperforms competitive baselines in closed vocabulary settings while being 100x smaller in size. Our model can effectively guide open-set object detectors like GroundedSAM to enhance open-vocabulary performance. We validate our approach through real-world RGS experiments using a 7-DOF robotic arm, achieving 90.33\% visual grounding accuracy in 15 tabletop scenes. Our codebase is provided here: https://github.com/vineet2104/hifics