Juicebox-Pro does what it can to prevent users from easily downloading images but, ultimately, anything that is visible on the internet can be saved.

Right-clicking is disabled within a Juicebox gallery (so a visitor will not be able to save gallery images via the right-click context menu) and you can choose to not display the Open Image Button or the Download Button in a gallery by setting showOpenButton="FALSE" (in the 'Lite' options section) and showDownloadButton="FALSE" (in the 'Button Bar' options section) respectively, as noted in this FAQ:
How do I allow or prevent users from saving gallery images?

Unfortunately, there's nothing you can do to prevent users from taking screenshots of your galleries but, as a deterrent, you might like to watermark your images.
If you create a gallery with JuiceboxBuilder-Pro and use the Watermark functionality, then the chosen watermark image is actually embedded into the main images at the time the images are resized for the gallery, so if a user does find the URL to an image on your web server, the image will be watermarked.

I'd also recommend that you keep your image resolution as low as possible (high enough for web gallery use but too low for other uses such as printing).
This should hopefully discourage visitors from trying to download your images.

Anything more that you do to prevent a user from downloading an image from your web server will more than likely also prevent Juicebox-Pro from displaying it.