Crossword Genius

What soldiers (at the double) say as they leave (2-2)

Ross

I believe the answer is:

ta-ta

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

'they leave' is the definition.
The definition suggests a singular noun which matches the answer.

'what soldiers at the double say' is the wordplay.
I cannot quite see how this works, but
'soldiers' could be 'ta' (abbreviation for Territorial Army) and 'ta' is located in the answer.
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is found within the answer.
A single letter 'a' remains which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

'as' is the link.

Can you help me to learn more?

(Other definitions for ta-ta that I've seen before include "Bye-bye" , "Cheerio" , "Adieu" , "A Farewell" , "Bye!" .)

I've seen this clue in the Evening Standard.
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