M.P.
I would try paying no attention to it for awhile, perhaps a couple of weeks and see if that helps. When something becomes a "big deal" as evidenced by Mom's commenting on it, somehow doing it stays in the front of the mind and it becomes harder to quit. It can also become an unrecognized or even a recognized power struggle.
I've noticed that with myself. When I notice that I'm clearing my throat more often I can't seem to stop. When I stop noticing it goes away. As a child I started burping. The more I burped the more I did it. My aunt would tell me to stop and I couldn't. Once everyone stopped paying attention, in a couple of days I not only stopped but I realized I was making it happen. I think this worked because burping became my problem to figure out. Of course, burping all the time was uncomfortable for me. It had become a nervous habit. Our family was split up with me and my brother living with an aunt and uncle.
Could your daughter be anxious about something and this is a way of self-soothing?
My 10 yo granddaughter chews her hair. She and her mother have been told that she's a sensory person who needs to be doing something with her mouth to help her focus. She's been diagnosed with ADHD and was in a special writing class this past year. Students are allowed to chew gum in that one class only and it did help her stay focused on her writing while she continued to have a difficult time staying in her seat in the regular classroom.
Her mother asks her to take her hair out of her mouth, over and over during the day and evening. She takes it out for perhaps 10 minutes and it's back in her mouth. So, I suggest that telling her to take her fingers out of her mouth is apt to not work.
It could be that she's just discovered that sucking on her fingers is comforting. I don't know if your daughter would benefit from having something in her mouth but you could try having her chew gum or suck on something.