The phrase "gives the once over" typically means to give something or someone a thorough inspection or examination. Its antonyms would be phrases that suggest a lack of inspection or examination, such as "ignores," "neglects," or "disregards." Other antonyms might include phrases that imply a lack of attention to detail, such as "skims over," "glances at," or "passes by quickly." Essentially, any phrase that suggests a quick or cursory examination could be considered an antonym for "gives the once over," as this phrase implies a slow and thorough examination of something or someone.