That would be Antidoron. It is a sharing of Christian love via bread with those who did not commune.
Interesting. As best I remember, Antidoron was not offered to Non-Communicant external Attendants (such as myself) at the Antiochan Orthodox church which I attended.
I took no offense at this, of course, recognizing myself to not be an Eastern Orthodox Communicant. But perhaps customs differ from parish to parish.