Antonyms for the phrase "give a tumble" would include phrases such as "ignore," "disregard," "overlook," "neglect," "brush off," or "dismiss." These terms refer to the act of choosing not to put attention, effort, or importance into a situation or person. Conversely, the meaning of "give a tumble" suggests giving a matter some consideration, attention, or perhaps assistance. It is often used to describe a process of recognizing or becoming aware of something, or taking the time and effort to engage with and understand something more deeply. Antonyms for this phrase reflect a lack of interest or involvement in a given topic.