If you're looking to be able to edit the permission and privacy settings on all drops on your team (or change them based on role/group within your team), please review our teams offering: www.getcloudapp.com/pricing.
Your drops are always safe with us, but for increased security, you can follow these steps to adjust the share settings for your drops in both the desktop and web app.
Web App for new drops (go to Account Settings -> Link Setting).
You can also change all the links to your existing drops into private, but remember that this will break all existing public links (your drops will still be online). So anyone who was using the public link before will no longer be able to access it.