Antonyms for the phrase "hath bearing on" are "irrelevant," "unrelated," "unconnected," "extraneous," "immaterial," and "nonessential." These words suggest that something is not pertinent, applicable, or significant to a particular situation or question. For instance, if someone asks about the impact of social media on mental health, details about the weather would be considered irrelevant or unrelated. Likewise, if a company seeks to hire a marketing manager, an applicant's knowledge of astronomy would be extraneous or nonessential to the decision. By using antonyms for "hath bearing on," we can more accurately describe what is and is not relevant in different contexts.