After much thought (pun intended), I feel that, although this, along with much else in the game, is ultimately left up to the DM's prerogative, it would be best to view this in the context of a Kenku character who was deaf. In this case, it would certainly be able to receive the thoughts of another who was listening to something, but, although the actual sounds might be transmitted, the Kenku would have no reference and would thus be unable to repeat the sounds.
The reason I believe that exercise is helpful is because it is an extreme example of a person's (or character's) perception versus reality. For instance, when I and a friend of mine listen to a song, I will hear the guitar and drums, but struggle to hear the words. However, my friend will hear the words quite clearly and would not, for the life of her, be able to recall or repeat the guitars. So, if she were to communicate the song telepathically to the Kenku, it would hear only what she heard...assuming telepathy transmits the sounds and not a description of the sounds (the reason we probably should require DM intervention), and would only have one person's filtered experience of the song.
On a side note, having the Kenku "hear" something from several different characters might be the only way for it to accurately repeat a sound.