T.,
It's obviously a source of comfort to your daughter to suck her finger, and very convenient since she has it nearby at all times. I wonder if you could help her better by telling her that growing up doesn't mean you stop needing comfort, it just means finding different ways of getting it. Even though she told you she doesn't care who thinks what, she maybe privately does. But it's just like any other behavior. You can't just tell them to stop, you have to help them find an acceptable substitute.
How about worry stones - maybe give her one to keep in her purse, and for each coat pocket. Suggest that every time she gets the urge to suck her finger, she try to remind herself to use the worry stones. Another idea might be a silver bangle for her wrist that she can rub and turn when she needs to calm herself.
At least your daughter's coping mechanism is something you can see - so you can help her move to something more appropriate. My daughter was a closet bulemic, something we didn't figure out for a few years!
Good luck!