The phrase "giving once over" means to give a cursory or quick look at something. Antonyms for this phrase would be "scrutinizing in-depth" or "thoroughly examining." These antonyms suggest that a more careful and detailed inspection is required, rather than just a fleeting glance. Other antonyms might include "ignoring," "overlooking," or "dismissing," which imply a lack of attention or interest. In a professional context, it's important to use the appropriate amount of attention and effort when examining something, whether it's a document, a product, or a situation. Choosing the right antonym for "giving once over" depends on the level of scrutiny or detail required.