Like all of the Canterbury Tales, there are several different ways you can choose to read each individual tale.
One way might be to compare "The Manciple's Tale" to similar tales in the collection, and the talking crow seems - at first, at least, very similar to Chaunticleer in "The Nun's Priest's Tale".
This is because, I think, the Manciple's tale begins looking like a fun, fantastical tale with no serious consequences just like the Nun's Priest's: a fantastical, mythical figure in Phebus (god of poetry), an emphasis on music and enjoyment, and a comical, talking animal.
But unlike the earlier tales where adultery is a comical subject (think of the Miller's Tale!) Phebus' reaction to the bird's truth-telling provokes, not a comic reaction, but a vicious, brutal act of a realistic violence. This act of violence robs the crow of its speech: turns the comic, fantastical creature into a recognisable crow.
The Manciple raises questions of when to speak, and when not to speak, and whether it is always right to tell the truth. In the crow's taste, as the Manciple creepily reiterates at the end of the tale, the best advice is to keep your mouth shut. It is better, the Manciple says (in his told, aural story) not to speak at all.
And I would argue that - at the end of the Canterbury Tales, as the revelry is coming to an end - falling into silence is precisely the theme of the Manciple's Tale.