Eliza (the girl) was insisting to pay for her lessons even though Higgins did not demand it. It was due to the hesitation of Higgins to teach her to speak gently. Eliza deciphered this as Higgins reluctance of not working for free since he must have thought that poor flower girl won’t have enough to pay for his speaking course.
To clear the air regarding the same, Eliza kept insisting for following a professional approach where she would pay for her speaking course.
If you open a parenthesis, you need another to close it! Note: In technical writing, there are additional rules for using parentheses, which can be more nuanced
