In recent years, the awareness of the academy around responsible research has notably increased. For instance, with advances in machine learning and artificial intelligence, recent efforts have been made to promote ethical, fair, and inclusive AI and robotics. To better understand if and to what extent HRI is incentivizing researchers to engage in responsible research, we conducted an exploratory review of the publishing guidelines for the most popular HRI conference venues. We identified 18 conferences which published at least 7 HRI papers in 2022. From these, we discuss four themes relevant to conducting responsible HRI research in line with the Responsible Research and Innovation framework: ethical and human participant considerations, transparency and reproducibility, accessibility and inclusion, and plagiarism and LLM use. We identify several gaps and room for improvement within HRI regarding responsible research. Finally, we establish a call to action to provoke conversations among HRI researchers about the importance of conducting responsible research within emerging fields like HRI.