Corrupt? Oddly, they're overwhelmed by praise (10)
I believe the answer is:
adulterate
'corrupt?' is the definition.
(to adulterate is to mix with something else)
'oddly they're overwhelmed by praise' is the wordplay.
'oddly' indicates alternate letters (letters in the odd-numbered positions are used).
'overwhelmed by' is an insertion indicator (inserted letters get absorbed or overwhelmed).
'praise' becomes 'adulate' (adulation is praise).
The alternating letters of 'theyre' are 'ter'.
'ter' going within 'adulate' is 'ADULTERATE'.
(Other definitions for adulterate that I've seen before include "Reduce purity" , "Spoil" , "Debase by adding inferior material" , "Make impure by addition" , "Make poorer by adding another substance" .)