What you will have to do is to make those grid lines in the Photoshop file itself. As you know, those gridlines won't print and won't save in the .jpg file. So you should create another layer on top of your image, and then trace the grid lines. You can use the pen tool (make sure to select Paths, which is the middle icon of the three small icons up in your option bar near the left corner when the Pen tool is active.) Then you can stroke each path, in the color you want.
An alternative is to use a very fine hard brush in the color you want, and trace the gridlines that way. If you hold down the Shift key it will constrain the brush lines to 90 degree and 45 degrees, so you should be able to do straight horizontal and vertical lines as needed.
Once you've traced the gridlines, you can flatten and save as a .jpg file that you can give to people as needed.
If there's another way to preserve those gridlines, I don't know it!