Agent responds, overlooking false statements (3)
I believe the answer is:
rep
'agent' is the definition.
(short for representative)
'responds overlooking false statements' is the wordplay.
'responds' becomes 'replies' ('reply' can be a synonym of 'respond').
'overlooking' indicates named letters should be taken away.
'false statements' becomes 'lies' (lie is a kind of false statement).
'replies' with 'lies' taken out is 'REP'.
(Other definitions for rep that I've seen before include "Fabric with a ribbed surface" , "Corded fabric" , "Repertory theatre" , "Travelling salesman" , "Theatre; fabric; salesman" .)