I would encourage you to welcome this kid into the party. By doing so, you could teach your child the value of being inclusive even towards people we do not hit it off with. This other child might be feeling left out and might have even told her parent that she was invited. Or the parent might be feeling like her child is being left out and trying to look out for her by putting you in a position that is a little awkward, but that gives you the chance to extend grace.
I come from a culture that tends to be very inclusive, very group oriented. Inviting several people out of a group, means inviting the whole group, and you just better be prepared. But I have lived most of my life in the US, where the expectation is that you only go to a party if you are explicitly invited.
I find that the group oriented culture, in this factor, has a lot of positive value. I have used that to teach my children to be kind and welcoming even to kids that they would not normally gravitate towards.
You have a great chance here to teach your child grace and kindness to someone that may be feeling left out. I suggest you take it. A word of caution, if you do choose to extend this grace to the other child, the truly gracious thing to do is to not say a word about it to either the other child's parent or the other child. And you will need to make sure your child understands that.