Crossword Genius

Wear down that woman in East End with poem (5)

Ross

I believe the answer is:

erode

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'wear down' is the definition.
(to erode is to wear down or decay)

'woman in east end with poem' is the wordplay.
'woman in east end' becomes 'er' (I can't justify this - if you can you should believe this answer much more).
'with' is a charade indicator (letters next to each other).
'poem' becomes 'ode' (ode is a type of poem).
'er'+'ode'='ERODE'

'that' is the link.

Can you help me to learn more?

(Other definitions for erode that I've seen before include "Abrade" , "Wear away with weather" , "Grind down" , "Gradually wear away" , "Slowly remove" .)

I've seen this clue in The Mirror.
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