During this time, between ראש השנה and יום כפור , the common greeting seems to be גמר חתימה טובה. (According to a shiur הרב יעקב משה קולפסקי, זצ"ל used to say over, it might still be appropriate to use the popular pre-ראש השנה greeting, כתיבה וחתימה טובה. But אין כאן מקום להאריך.) However, the gender of this greeting puzzles me. What is it that we are wishing? Should it be a גמר of a חתימה טובה? Or, are we wishing that the גמר חתימה be a good one? The shortened version of this greeting, גמר טוב, would seem to indicate that it is the latter. If so, should the greeting not be גמר חתימה טוב?!
It could be that the general public is thrown off by the word חתימה to think that the term, as a whole is feminine. Nevertheless, see this Kashrus Kurrents article and footnote 1 regarding proper grammar vs. common convention.
Well, whatever the proper gender is - it should all be for the good!