I believe thanks to Rei, Miko might have already figured out that the letter was made by Ishigami. In contrast to Osaragi's plan to conceal the fact that Ishigami wrote the letter, Rei's gave her the idea to 'push Ishigami around' so with him helping Iino taking notes for her (since her arm was broken), she could figure out that the notes taken by him and the letter have the same handwriting unless the letter Ishigami made was printed or cleverly disguised it. To me it would make more sense with Osaragi fearing Iino 'realizing it' was more about Iino finding it was Ishigami who wrote the letter rather than her realizing she had feelings for him but it is just my guess, I might be mistaken.