Federated Learning (FL) is a promising machine learning paradigm that enables participating devices to train privacy-preserved and collaborative models. FL has proven its benefits for robotic manipulation tasks. However, grasping tasks lack exploration in such settings where robots train a global model without moving data and ensuring data privacy. The main challenge is that each robot learns from data that is nonindependent and identically distributed (non-IID) and of low quantity. This exhibits performance degradation, particularly in robotic grasping. Thus, in this work, we propose MTF-Grasp, a multi-tier FL approach for robotic grasping, acknowledging the unique challenges posed by the non-IID data distribution across robots, including quantitative skewness. MTF-Grasp harnesses data quality and quantity across robots to select a set of "top-level" robots with better data distribution and higher sample count. It then utilizes top-level robots to train initial seed models and distribute them to the remaining "low-level" robots, reducing the risk of model performance degradation in low-level robots. Our approach outperforms the conventional FL setup by up to 8% on the quantity-skewed Cornell and Jacquard grasping datasets.