Android Question Dynamic App icon

Generally, the only way to do that is to remove and replace your icon's shortcut with a new one. That would mean that they'd have to have 31 different icons in their APK. If you're looking to modify the icon's badge, then you can use something like this: https://www.b4x.com/android/forum/threads/shortcutbadger-v1-7.64305/

If they don't have 31 app icons in their apk then I suspect the calander "app icon" may be a widget and not an actual app shortcut.