text input not text box. the text input object is the one you can type in. it has a permanent white background and no obvious way to turn that off. A text box (one that can't be typed into) does by default have a transparent background.
I don't use C3 really but in C2 the textbox is the object with the white background, text is transparent. To make the textbox transparent, well you got your answer in that original topic? Set CSS style is in the textbox events. Answer is already there, not sure what other info you need.