Typically, you can force the download of content on standard browsers by setting headers
"Content-Disposition", "attachment; filename=\"LicenseAgreement.pdf\""
on the return. This SO shows how to return a PDF file but theoretically, you could do the same with an image.
How can I present a file for download from an MVC controller?
However, it is questionable if every browser that is supported by jquery mobile would even respect that and give any kind of a save prompt or just open the image in a new window. Give it a shot but test it on iOS, Android, WinPhone 7.5+, and (gagging) Blackberry 6+ and see what happens because they're probably going to all behave a little differently.
Were it me, I'd simply link directly to the image either on the current page or with a target="_blank" and let them save it however they usually save images.