The Hebrew word for conversation is שִׂיחָה (see-KHAH).
The word for conference is וְעִידָה (ve-ee-DAH). It comes from the same root as the word for committee - וַעַד (VAH-ahd) and its synonym, וַעֲדָה (vah-AH-dah). ועדה also carries the meanings, board and commission.
Anyway, a conference call is a שִׂיחַת וְעִידָה (see-KHAHT ve-ee-DAH). This means, literally, a call of conference. The ה in the word שיחה turns into a ת as the שיחה and ועידה are connected, grammatically, with this notion of belonging - the word of implied.