Kind of a workaround, but on the website, if you go to your My Account page and click on the link on the left that says My Hilton Honors Card, it will pop up a window pointing you to the Android or iPhone apps. That window has an image of your physical card, with your expiration date at the bottom. You can also choose to print the image or save it as a .png file. All of these have the expiration date. (or, you can request that a physical card be mailed to you.)