Follow along with the video below to see how to install our site as a web app on your home screen.
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If you've been syncing your Note's Contacts with your Google account, you can use a web browser and go to:
https://contacts.google.com
Log into your account, and in the left side panel tap on the little '>' link next to 'More', and in the contextual menu that pops down select 'Restore contacts'. There are options for how long back you want to go but it's not indefinite so hopefully it wasn't too long ago when you realized that particular contact was deleted.
If you use a different email service and your Contacts app is synced with that instead, hopefully there's a similar way to access old contacts.
If you've only been keeping your Contacts on your phone and you don't have them backed up anywhere I don't think there are too many options for you to recover deleted entries.