You do have to send your SAT scores directly from the College Board.
The high school is free to organize its transcripts however it see fit. You can always ask them to remove the SAT scores from for transcript; the worst they can say is “no.”
The good news is that colleges are just going to consider your best scores.
Yours is a common situation. Students here about score choice with the College Board and believe they can withhold scores only to find out that there are still many high schools that put all your scores on your transcript sent to colleges. Thus, excercising score choice with the testing agency when sending offical scores accomplishes nothing except to provide evidence that you intentionally tried to withhold scores not knowing your high school transcript would have them
Many, many years ago almost all high schools put test scores on transcripts, including becausee most colleges accepted the scores provided on the transcripts and did not require official scores from the SAT and ACT testing agencies. Over the years, more and more colleges adopted the requirement that you provide official scores from the testing agency to the point that today only a minority accept scores on the transcript. In the last 15 to 20 years or so, more and more high schools have stopped putting scores on transcripts but there is still a very large number that do. Your recourse is to ask the high school to not put them on the transcript sent to colleges but high schools may not do that.
If it is any consolation, the rule followed by colleges when you submit scores from multiple tests is to use your highest scores (depending on college, either that test with the highest composite or the highest secition scores for the multiple tests) and do not hold lower scores against you.