The phrase "gave heed to" suggests paying attention or listening carefully. Its antonyms would be phrases that indicate a lack of attention or interest, such as "ignored," "disregarded," "neglected," or "overlooked." When someone ignores or disregards a piece of information, they are not giving heed to it, while neglecting something suggests a more ongoing lack of attention. Overlooking something implies not noticing it at all, rather than intentionally ignoring it. In any case, the antonyms of "gave heed to" imply a lack of interest or inattention, which can lead to missed opportunities or misunderstandings.