should you try to correct a kata that someone outside your school but in the same system is doing? I think this might be a tricky situation but I might ask why it was being done the way the person is doing it and why the changes
I don't think so, no. You're not their teacher. As you say, I might ask questions, but I also know that the answer is likely to be "because that's how my teacher wants it done". I'd be more likely to ask their teacher, if I had the chance, but even then the answer may well be the same.
Here's an example. In the TKD yudanja form Keumgang, a crane stance with a diamond low block is done several times.
In the KKW version of this for, the leg is drawn up quickly while the blocks are performed slowly. In some schools, students are taught to squat before rising up to the cane stance. In our school, the foot rises slowly, reaching the final position at the same time as the hands.
My understanding is that the reason for doing the blocks slowly is to force the student to hold the crane stance longer, as a balance exercise. (Part of the meaning of "keumgang" is "immovable" and balance is one of the things we must perfect if we're to be immovable.) My KJN believes the balance exercise is made more effective if the foot moves slowly, since the more body parts moving, the more difficult maintaining balance is.
I practice it his way and the KKW way, and while discussion is always welcome, I'm not likely to accept correction from random people.