To create a file you can use with other programs, you need to export it.
To make the green and red control points disappear before you export the image, select "Update Georeferencing" from the Georeferencing toolbar:
To create a transformed image file that can be used in other programs, select “Rectify…” from the Georeferencing toolbar then save the picture with a new file name: This image used the "3rd Order Polynomial" transformation
Give your file a meaningful name:
You can also zoom into a portion of the image and save it by going to "File" and then "Export map..." This image used the "Adjust" transformation