The phrase "have dibs on something" means to claim exclusive rights or ownership on something. Its antonyms, or the opposite phrases, would be to relinquish or surrender those rights to someone else. These include phrases like "give up," "yield," "cede," or "relinquish." Other antonyms could be "share," "divide," or "distribute," indicating a willingness to split ownership or usage of something with others. Furthermore, the phrase "have no claim" or "not entitled" could serve as an antonym, indicating that there is no exclusive right or ownership for an item or opportunity.