The correct answer is "That music reminded me (I remember it well) about the adventure we had"
Step-by-step explanation:
According to grammar, one of the uses of parentheses is to enclose information that serves as an explanation, illustrates, provides examples or clarifies an element in the sentence and the information enclosed does not grammatically fit with the sentence and is non-essential to it. According to this, in the case of the sentence "That music reminded me I remember it well about the adventure we had" a parentheses should be used to enclose "I remember it well" because this information just clarifies the main action "reminded me" but does not fit grammatically with the sentence or is essential to it. This implies the correct revision is "That music reminded me (I remember it well) about the adventure we had".