Lily was annoyed that there wasn't a clear cut answer to this. She was also annoyed that Dumbledore wasn't around to give them something resembling the right answer, the way kids expected their parents to have everything figured out from start to finish; though, as impressive as Dumbledore often was, he hadn't quite hit the omniscient stage yet she supposed. Even Moody would have some sensible suggestion to...
"Moody! What about Moody? Moody's been known to bounce about with Crouch, right? He'd be the right one to keep an eye on his inner office in the MLE, while Frank and Alice have the auror department. Moody could even whip up some bullshit assignments for Alice or Frank that have them interacting with Wilde's inner-department there, see if anything smells fishy. We can alternate patrolling and setting perimeter wards around Wilde and Bagnold's homes, just in case, and... Bagnold's still doing transitional work with Crouch from switching over power, and she still keeps her office in the MLE, right? Isn't your sister working with her, Ed? Would she want to help us?"