I'm really sorry that this is happening to your child and they're feeling this way! In my experience, both as an educator and, long ago, as a very adult-pleasing child at school myself, sensitive children take mild rebukes much more seriously than others. I'm going to assume, since you haven't said anything to the contrary, that your DC isn't a constant and deliberate rule-breaker but that the discipline policy in this classroom is a bit heavy-handed.
You might get a few comments about building resilience, but the difficulty is that to a child for whom this isn't natural, just being told that the strikes are deserved/they should get on with it/etc isn't emotionally helpful. What I'd advise (and what I think would have helped me as a child!) is that you tell your DC that getting strikes doesn't affect your opinion of him/her in any way, and that it doesn't make them a bad child or a bad person. Presently, helping them with confidence and self-esteem takes priority over telling them off for talking in the classroom - they're getting that at school already! Discussing it would be a good idea, but in a relaxed, non-judgemental way, since you don't want to exacerbate the anxiety.
Learning to deal with criticism (however much deserved) is very difficult for some children, and it's important that they know on an emotional level that it's the particular behaviour that's unwanted, not them as a person. It's difficult. Classroom management techniques are designed for the average child who probably wouldn't be as affected by the 'strikes' as your DC is. A one-size-fits-all policy might seem fair to the school, but it disproportionately effects the sensitive and conscientious.