My daughter is in 9th grade. I know she has a Spanish quiz which she showed me and I think gets to keep. Today she brought home a math test. She either had to or wanted to fix her mistake. I don’t think it changes her grade any. For this test it sounds like she has the option to retake the test (different paper) and hope she improves but will get the lower grade if that happens. I think she can only retake the test if she shows the teacher the corrections.
I have no clue though if she gets to keep either the original test or the retake (if she take it). I guess she could make a photo copy if she wanted to. I also have no idea what a test center is.
I remember when my oldest was in 3rd grade. She had to write spelling sentences every week. She never once got back any of her spelling sentence papers. I have no idea why the teacher would want to keep those.