Mum's out to do wrong, I see, but not a lot (7)
I believe the answer is:
modicum
'lot' is the definition.
(thesaurus)
'mum's out to do wrong i see' is the wordplay.
'out' is an insertion indicator.
'to do wrong' becomes 'od' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'see' becomes 'C' (the word for the letter, according to Chambers).
'od'+'i'+'c'='odic'
'mum' placed around 'odic' is 'MODICUM'.
'but not a' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for modicum that I've seen before include "Little bit" , "touch" , "suggestion" , "Mum, I cod about a small amount" , "Token amount" .)