UCAS Personal statement question about AI and Plagiarism Checkers, please help!

Hi, so I might be overthinking this massively here, but I recently finished my personal statement and put it through some free online AI and plagiarism detectors. Obviously, I didn't use AI to write my statement but it was more of a cover-all-bases sort of thing you know.
Anyway, the problem isn't with the results, the issue I have is that when I was talking to my head of year about lowering the plagiarism results (they were at a low level because I mentioned some classical books and a quote, and ideally I want them to be 0%) and just checking everything over, a friend who was there mentioned that they were told that having put it through the detectors would cause the statement to have a greater chance of being flagged by UCAS because it would now be on an internet database. My teacher didn't know anything about it so I've tried looking online to see if this is true and I can't find anything explicitly stating so, but now I'm mildly (very) concerned that I might have to rewrite the entire thing. It's not particularly an issue if I have to do so but my current statement was one I was very happy with and as I'm applying for an early application, I don't want to rewrite it quickly and end up with a lower quality statement in the end.
I might be being a little silly but I was really hoping someone would potentially be able to help me answer this, thank you for reading

Ahh thank you so much, that's really helpful to know! I was honestly dreading rewriting It all so that makes me feel much better lol, thank you for taking the time to respond to me, I really appreciate the help