I've been teaching for 21 years, the last 13 in reception. I'm now in year 1.
I've always been given invitations to put in book bags, and my school has no issue with this. With a class of 30 it would take about 5 mins to pop them in book bags. My personal rule has always been to do that job at break or lunch so the kids don't see them going in bags.
We do have circle times about things like not being invited to parties, or not being able to go to clubs etc, and I've had to stop many reception children writing lists of children who can and can't come to their parties when they have fallen out! (When it's not even close to their birthdays/ parties, it's just a way of exerting some control).
Now I'm in year one I haven't been asked to hand out any invitations. I think it only happens in reception cos the children are new to school and the parents don't know each other well enough to make contact out of school.
We are sensitive to the children's feelings and that's why we do the circle times linked to feeling left out etc, but also to make sure they know that sometimes they can't take part in something and that's ok - fair vs equal etc.
I don't think the handing out of the invites is the main issue, it's how your daughter is feeling about being left out. There are some lovely children's books about emotions and feelings, and it's fine to say to your daughter that it isn't fair but sometimes things aren't fair. I would do as other PPs have said and plan something else for her to do on that day instead.