A bit different but my kids deal with questions all of the time as to why they changed schools. They now go half way across the city to attend a congregated gifted program in a different school board than where they started out.
All of the neighbourhood kids still attend the neighbourhood school, all of the kids they play sports with and do activities with are all still at their old school or in a small number of schools close by. DS moved a year before DD so we also had a year where we were at the school for events after he had left which meant a lot of encounters with former classmates & their parents.
I think my advice would be to keep it simple and short. The more details my kids seemed to provide the more the other kids seemed to want to keep talking about it (and in some cases use the details to tease, etc). After much experimentation my DS10's go to answer is usually now "it's a long story" and then he changes the subject. There was one kid he's played hockey that was very fixated on it and teased him a lot last year and tried to turn the whole team against him. Any tiny detail DS provided was then used to tease him and used in rumours and taunts. Once DS switched to repeating the same basic statement and acting like it was no big deal the kid seemed to run out of ammo and moved on (the coaches also talked to him several times about picking on kids, etc which I'm sure also helped).
Of course we might have had the advantage of mostly dealing with 8 year old girls and/or 10 year old boys. Not sure how tenacious 10 year old girls would be in wanting to get to the bottom of things.
Since the underlying reason isn't something you necessarily want made public (and the school probably doesn't want to open the door to every parent wanting to move their kid either) I think I would just stick with something basic like "principal x decided to move me" or something along those lines. We also had long talks with our kids about why we might not want to go into huge detail and that it isn't because it is something to be ashamed of, or that they did anything wrong it is just easier to deal with potential mean people that way sometimes.
Not sure if that is at all helpful but good luck! Hope the change works out.
