The main treatment modality for oropharyngeal cancer (OPC) is radiotherapy, where accurate segmentation of the primary gross tumor volume (GTVp) is essential. However, accurate GTVp segmentation is challenging due to significant interobserver variability and the time-consuming nature of manual annotation, while fully automated methods can occasionally fail. An interactive deep learning (DL) model offers the advantage of automatic high-performance segmentation with the flexibility for user correction when necessary. In this study, we examine interactive DL for GTVp segmentation in OPC. We implement state-of-the-art algorithms and propose a novel two-stage Interactive Click Refinement (2S-ICR) framework. Using the 2021 HEad and neCK TumOR (HECKTOR) dataset for development and an external dataset from The University of Texas MD Anderson Cancer Center for evaluation, the 2S-ICR framework achieves a Dice similarity coefficient of 0.713 $\pm$ 0.152 without user interaction and 0.824 $\pm$ 0.099 after five interactions, outperforming existing methods in both cases.