There are two things here. One is the "not enough effort". Teachers do get that wrong sometimes, especially with the quieter ones. I always used to begin parents' evening with "so what's he/she said about maths", because I didn't want to leap in with my comments if actually the child was in tears over their homework. At the meeting for my DD's most-hated subject, her teacher kicked off with "DD enjoys geography"!
The other issue is the message about whether she has the potential. Most kids do have the potential to get there eventually, but the problem is that the education system wants them to get there by 16. If the teacher thinks she is not on course to get the maths grade she'll need for science A-levels, it's probably worth flagging up. Of course, you're already taking the sensible step of getting her some extra help in maths. Does the teacher know that? It may make the difference, as you've still got plenty of time.
Be aware that there are alternative routes to A-level. It may be that in the long run, BTec Science may suit your daughter better than A-levels. It's far too early know or to be making decisions yet, but keep it in mind. A private school is unlikely to offer BTecs, so they may be more inclined to think in terms of A-levels or nothing!
I'd ask for a meeting/call with the maths teacher. Check out whether she's concentrating in lessons, what they think needs to change in terms of effort. Sometimes a child with a tutor switches off at school because they feel the tutor will solve all their problems - I'm not saying your daughter is doing this, but just check in case. Or she may just be a bit chatty, and the comment wasn't meant to mean that she makes no effort, just to warn her not to get distracted. Also ask the teacher if they know where her weaknesses are, although the tutor may be better able to establish this as they are working with her one-to-one. Often struggles with maths are down to something earlier on that wasn't fully mastered or understood - fluency with tables, really understanding fractions and their relationship to division, negative numbers are all common ones.
It's best if the tutor does not follow the topics your daughter is doing in school, but focuses on areas of difficulty and things they are not doing at the moment (which helps retention). Flashcards are not particularly helpful for maths (although there are some facts that need to be remembered) - what helps most is practising doing questions.