And how is that supposed to help the OP, exactly? She is asking for advice. Are you suggesting that she should just write off her child as a bully at 7 and leave it at that?
OP, it sounds like you've had a conversation with your child already about why they said that and how it might feel to be the other child etc. And you've said that there was at least some remorse, so that's good.
Personally, I wouldn't go down the route of punishing them for what they said, but I would ensure that they knew I was upset and disappointed by their behaviour because of the hurt that they might have caused to the other child.
I think I would be inclined to revisit the conversation. Tell them that you have been thinking about what happened and that you're sure your dc must know something about why they said what they did. Did they think it was funny? Were they trying to hurt the other child? I don't think I would allow "don't know" as an answer - I would want to push quite hard to try and get to the bottom of the situation and to talk a bit more about what led to the incident.
I might also have a chat with the school to find out what dc's behaviour was like in general, and more about their relationship with the child in question, whether they had any insights into the situation etc. And I would ask to be told about any further incidents or issues involving my dc, no matter how small.
Finally, I would keep an open mind. It might indeed be that your child was bullying the other dc, and you should therefore be vigilant for any signs of further bullying behaviour. On the other hand, it might be that your child has been on the receiving end of bullying from the other child, and that this was a rather misjudged attempt at fighting back.