Can You Stop People From Reblogging Your Tumblr Pictures?by James Wright
Reblogging is Tumblr's primary method of public communication, and this feature cannot be disabled. Any posts made public can be reblogged by anyone who can see them whether or not they follow you. However, by changing the visibility of your posts, creating a private blog or ignoring certain users, you can prevent your posts from being reblogged or reduce the likelihood reblogging will occur.
Change Post Visibility
When creating or editing a post, you have the option to set its status to private. Only you can see a private post; as a result, no one else can reblog it. If you make the post visible again, other Tumblr users can reblog it.
Create Private Blog
While your main blog must remain public, you can create a password-protected secondary blog. The audience of a private blog consists only of people you have approved and given the password. Only they can see or reblog a post you make to a password-protected blog.
Ignoring a user prevents her from seeing any of your posts in her feed. It doesn't prevent her from reblogging your posts, but it can serve as a deterrent. To see your blog's content, she must visit your blog by typing your URL into her Web browser.