Is this bullying?

[Bazinga2022]

my DD is in her first year at secondary school, she has a best friend from primary school there with her. Her and her best friend haven't really made any new friends since starting secondary school, I've been quite worried about her and said she shouldn't rely on just one friend so much, she should make an effort to make new friends etc.
So about 2 weeks ago she told me another girl had been hanging out with them, I thought great finally another friend. Yesterday I read her WhatsApp messages to her old friends from primary(she knows I do this every now and again to make sure she is safe), she has told them that her and her best friend had made this new friend cry, but she deserved it because she is kind of annoying.
I have sat her down and spoken to her about this and she said the girl kept following them about and they told her they wanted some time on their own, and walked away from her and she started to cry. I feel so bad for the girl just trying to make some friends in a new school.
I have spoken to my DD and she doesn't even seem that bothered that she made someone cry, but has promised to apologise to her on Monday. I don't want her and her best friend branded as the 2 mean girls at school, not sure if I should be punishing her for this?

Sounds mean to me. I would be asking her to think how she would feel in the other girl's shoes.

I would also be taking the phone as a consequence for the day.

Thank you. I have reminded her that a similar thing happened to her a couple of years ago where 2 friends didnt want her to play with them, i asked her to remember how she felt at the time, although she said it did make her sad at the time she still doesn't seem all that bothered.
I was thinking I should take her phone, I will do this now

I actually think this is a bit more complicated.
It depends on how it was said.
It’s hard because you don’t want them to exclude people and it’s right to say they should make an effort to be kind etc. but I also feel it’s ok for them to sometimes want it to be just them.
This other child may actually not be a good fit for them as friends. Maybe as they’ve got to know each other better they’ve realised they don’t have much in common. I wouldn’t expect any one to force themselves to be friends with someone. Being friendly is to be encouraged but it’s ok to not want to spend all your time with someone.
I personally wouldn’t be punishing her for this. I’d have a chat and lay down some expectations.
I would suspect punishing her for this will not increase her empathy for the other girl. Probably the opposite actually.