If you have no delete button available from a Tag open in SharinPix administration dashboard, that could be normal.

You can delete tags that are not used anymore. So to gain back the delete button, you should first untag all the pictures using this tag and then get back to the administration dashboard to see the delete button back.

Within the administration dashboard you have a Tag Image related list which list all the images using this tag. A tag could be deleted ONLY when this list is empty.

Navigate from there to find the images to untag and get back here as soon as you have remove all the Tag Image.