All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
You have done well when you clarified to your aunt that it is impermissible to commemorate one's birthday or to give and accept gifts on it, or to distinguish that day from the other days. However, since she declared that her gift to you was not for that occasion, then it would be permissible for you to accept it and benefit from it. Since you have repaid your debt from it, then you are acquitted from that debt and nothing is due on you.
As regards the Bid‘ah (religious innovation) of celebrating birthdays, then it is done by the people in imitation of the West. So, it is impermissible to do it; and it is obligatory on a Muslim to clarify to his family that it is unlawful with wisdom and kind instruction. For further information, please refer to Fataawa 81725 and 124431.
Allaah Knows best.