Tumblr offers users the option to reblog posts in order to share them with friends and followers. This is an automatic feature and can't be disabled in your settings. If you prefer to disallow other users' ability to reblog your posts, edit the HTML code of your blog's theme to remove the reblog option.

Check the Code

Under the Tumblr dashboard of the blog you wish to edit, click the "Customize" link in the right column. Select "Edit HTML" in the left column to display the source code of your blog's theme. You can make changes and edits directly in this code to alter your theme's appearance and behavior.

Find and Delete

To remove the reblog option in your blog, press "Ctrl-F" to open a search box. Type "{ReblogButton}" without quotes and press "Enter." Delete this code everywhere it appears in your HTML text to remove the reblog button from your blog. Click "Save" when you're finished.