Hi Jake, back home now and batteries replaced. The nest protect chirped for two weeks and annoyed my neighbours somewhat! To be honest it would seem easy to add a remote silence option to the app to resolve the issue. The app allows all manner of remote actions so one more!!! This has to be a common problem, probably going unreported.
Sorry to hear it bugged your neighbors so much. I will be sure to provide this feedback to our Team, as we are always trying to improve our products. There is always a good chance that it could be released in future updates, and I do appreciate the feedback. Please let me know if you have any other questions from here.