The phrase "gives eyeteeth for" is an idiom that means to want something very badly. If we're looking for antonyms, i.e. words with contrasting or opposite meanings, it's important to first consider what this phrase implies. 'Giving one's eyeteeth for something' indicates an intense desire or longing for it. Therefore, its antonyms would suggest a lack of interest or indifference. 'Uninterested,' 'apathetic,' 'disinterested,' and 'bored' are a few opposite words that fit the bill. Alternatively, you could choose synonyms for 'content,' 'satisfied,' or 'unimpressed.' These words could serve as antonyms to 'gives eyeteeth for' since they suggest a lack of intense desire.