The industrial Internet of Things (IIoT) under Industry 4.0 heralds an era of interconnected smart devices where data-driven insights and machine learning (ML) fuse to revolutionize manufacturing. A noteworthy development in IIoT is the integration of federated learning (FL), which addresses data privacy and security among devices. FL enables edge sensors, also known as peripheral intelligence units (PIUs) to learn and adapt using their data locally, without explicit sharing of confidential data, to facilitate a collaborative yet confidential learning process. However, the lower memory footprint and computational power of PIUs inherently require deep neural network (DNN) models that have a very compact size. Model compression techniques such as pruning can be used to reduce the size of DNN models by removing unnecessary connections that have little impact on the model's performance, thus making the models more suitable for the limited resources of PIUs. Targeting the notion of compact yet robust DNN models, we propose the integration of iterative magnitude pruning (IMP) of the DNN model being trained in an over-the-air FL (OTA-FL) environment for IIoT. We provide a tutorial overview and also present a case study of the effectiveness of IMP in OTA-FL for an IIoT environment. Finally, we present future directions for enhancing and optimizing these deep compression techniques further, aiming to push the boundaries of IIoT capabilities in acquiring compact yet robust and high-performing DNN models.