When 참 means "so" or "very", it usually comes before an adjective or adverb or verb with such a meaning (참 잘한다, 참 좋다).
If it's used independently as in your example, it is an interjection to the effect of "Oh! I just remembered" that you utter when you suddenly remembered something or when you need to switch to a new subject. In your example, it is a little like "by the way". It is a different usage unrelated to "so" or "very".