Crossword Genius

What the pigeon said on Tuesday to another bird (4)

Ross

I believe the answer is:

coot

I'm a little stuck... Click here to teach me more about this clue!

'bird' is the definition.
(I know that coot is a bird)

'what the pigeon said on tuesday to another' is the wordplay.
I cannot really see how this works, but
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is present in the answer.
'another' could be 'o' (I've seen this in other clues) and 'o' is found within the answer.
The remaining letters 'co' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for coot that I've seen before include "Blackish aquatic bird" , "Proverbially bald aquatic bird" , "Bird said to be bald" , "Supposedly bald bird" , "Water bird of rail family" .)

I've seen this clue in the Evening Standard.
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