Raise objections (8)
'raise objections' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for demur that I've seen before include "Protest mildly, show reluctance" , "Waver" , "Raise scruples" , "Cavil, dispute" , "'Object, show reluctance (5)'" .)
(Other definitions for complain that I've seen before include "Find fault" , "Express dissatisfaction" , "Bemoan" , "Grumble, moan" , "Make objection" .)