Captialize “Hilton Honors” but not “the” or “app.”
The Hilton Honors app supports only iOS and Android. When referring to it by a name other than “the Hilton Honors app,” say “Our app for iOS and Android.”
“Our iOS app” and “our Android app” are acceptable but incomplete. Mind your context. “Our mobile app” is increasingly acceptable, but keep in mind that there are still other mobile OSes out there.
“The app” and “our app” are only acceptable after the first mention or within the app itself.