Many temples in South India dedicated to Ganapati maintain dovecotes. For instance,
A simple Google search on 'Ganapati Temple Pigeon' will give many such results. I faintly recall my mother saying something about 'prāsēva' (pigeon seva, literally) at Ganapati temples, but she does not know the details either.
What exactly is the connection? I am looking, in particular, for a reference from scripture.