Letter to be burned: react badly (9)

I believe the answer is:

character

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'letter' is the definition.
(written character)

'burned react badly' is the wordplay.
'burned' becomes 'char' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'badly' is an anagram indicator (letters in the wrong order).
'react' with letters rearranged gives 'acter'.
'char'+'acter'='CHARACTER'

'to be' is the link.

Can you help me to learn more?

(Other definitions for character that I've seen before include "constitution" , "case" , "Someone in play" , "Part" , "Quality" .)

I've seen this clue in The Times.

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