The antonyms for the phrase "most wrapped-up" would be words that indicate a lack of involvement or engagement. Some possible antonyms could be detached, uninterested, apathetic, disengaged, or distant. These words suggest a lack of emotional investment or enthusiasm for whatever is being discussed or experienced. Alternatively, antonyms could be words that suggest a lack of preparedness or disorganization, such as unprepared, scattered, or unfocused. Whatever the specific antonym, it is clear that the opposite of being "most wrapped-up" is to be disconnected, disengaged, or uninvolved.