Does informing my grandmother that I have completed memorizing the Quran—so that she may receive the reward—fall under showing off or diminish my reward?

You are not obliged to inform your grandmother that you have completed reciting the Qur'an, and she has no right to demand it. While it is obligatory to show kindness and dutifulness to your grandmother, you are not required to obey her in matters where she has no valid reason, especially if her command contradicts what the Shari'ah encourages, such as concealing good deeds. It is more complete and preferable for a servant not to inform anyone about their acts of obedience if they can avoid it, for the more a good deed is concealed, the closer it is to sincerity (ikhlas), and the more protected it is from defects like showing off (riya'), seeking reputation (sum'ah), and desiring worldly gain.

There is no basis for your grandmother's statement, "If you don't tell me, you are not forgiven [or I will not forgive you]." You should thank her for her concern and explain to her the reason that prompted you to conceal your completion of the Qur'an from her, and that this is part of perfect sincerity (ikhlas) and closer to acceptance by Allah.

As for informing others about your completion of the Qur'an, it is not by itself showing off (riya'). Riya' is: "intending people through obedience to Allah."