In the latest patch, it's currently impossible to complete this quest. I've spoken to Annie after clearing Caer Lem but she will only talk about the scavenger business, not this sidequest.
I've attempted to wait for the scavengers to clear Caer Lem, but Annie still won't talk about her quest after that.
EDIT to add: After the latest hotfix, this quest is working properly. Bug can be closed.