Crossword Genius

A word twice back at leaving (2-2)

Ross

I believe the answer is:

ta-ta

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

'a word' is the definition.
Both the definition and answer are singular nouns.
Maybe there's an association between them I don't understand?

'twice back at leaving' is the wordplay.
I cannot quite understand how this works, but
'at' is found in the answer.
The remaining letters 'ta' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?

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

I've seen this clue in the Sydney Morning Herald.
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