Hello @DLight, thanks for posting on our Community!
It sounds like you're trying to delete files (move out) from your Dropbox folder locally on your computer while our desktop app is running.
If you don't want those files in Dropbox, I'd suggest copying or moving them outside of your Dropbox folder and letting the desktop app sync until it syncs your changes and is reporting to be up to date in your menu bar/system tray instead of deleting them.
From there, you can sort your files according to your needs as normal.
I hope this helps!