The phrase "gave the onceover" means to inspect something thoroughly or examine it closely. Antonyms for this phrase could include "ignored," "neglected," "overlooked," or "disregarded." These terms indicate a lack of attention or scrutiny, as opposed to the careful inspection implied by "gave the onceover." Other antonyms could include "dismissed," "rejected," or "refused," which suggest a deliberate decision not to engage with something. In all cases, the antonyms for "gave the onceover" suggest a different approach to dealing with information or objects, one that prioritizes a superficial or cursory examination over a deep, careful analysis.