Please unprotect the images and try to delete the files. I have attached the Manual of the Camera where you can get the instructions to unprotect the images.
Page 95 of the manual says how to remove the write protection.
If it won't work as expected, please check if all the contacts on the memory card and in the camera are clean and shiny.
Two choices: If you normally get pictures from the camera by connecting it to your computer, remove the memory stick before making the connection.
If you normally get pictures by taking the memory stick out of the camera and putting into a card reader attached to your computer, use the "Copy" command in the Setup'Memory Stick Tool menu (see page 52 of the manual: http://www.fujifilm.com/support/digital_cameras/manuals/pdf/index/x/fujifilm_xe2_manual_en.pdf ).
