You don't need a mobile app to make physical transactions using your Hilton Honors Debit Card, but keep in mind that some online transactions may require you to authenticate a transaction attempt via the app.
You should also keep the app installed to manage your account and keep an eye out for suspicious activity.
Hilton Honors Debit Card doesn't require top-ups as it connects directly to your bank account. This means that you also don't need WiFi access or international data roaming that may incur charges.