What significant change does Hawthorne admit to making in the scarlet letter telling story contained diary?

Hawthorne doesn't actually admit to making a significant change in the "scarlet letter telling story contained diary" because there is no such diary in The Scarlet Letter.

The novel is presented as a historical fiction, with the narrator finding and interpreting a dusty manuscript containing the story of Hester Prynne and Dimmesdale. The narrator is separate from the story itself, and there is no indication that he altered the events in any way.

It is possible you are thinking of a different story or making a misunderstanding. If you could clarify your question, I might be able to help you better.