The only possible notification options are:
- ☐ You are mentioned in COMM.
- ☒ Portal under attack.
- ☐ Recruiting and faction activity.
- ☐ News stories.
- ☒ Game notifications (Portal under attack, etc.)
- ☐ Send me Ingress-related events, promotion information, offers, and news updates to my email address.
This is likely by design, as you either choose to be notified or to not be notified. Getting picky would require extra programming as well as keep you less engaged with the game since the game goes on with or without you. Every time you hear that Ingress sound come from your phone, you're reminded about it. Every time you get an Ingress Damage Report in your inbox, you're reminded about it.
So, no, there's no way to do this in Ingress, and therefore no way to do this with phone notifications. However, you are likely using a Gmail account. If so, then this is something you can do with e-mail notifications using Gmail filters.
When a portal has been destroyed, it is mentioned in the email with the following status:
You can take advantage of this to build a filter that filters out all messages without that text in them.
Go to your settings
Go to your filters tab
Find and click "Create a new filter" at the bottom of the page
Create a filter for Ingress e-mails that don't have the word "uncaptured"
Subject: Ingress Damage Report
Doesn't have: uncaptured
Select "Skip the Inbox" or "Delete it" to hide or auto-delete these e-mails
This should make it so that you only receive Ingress Damage Report e-mails for portals that have been destroyed into your inbox. All other notifications (including the ones leading up to the destruction) will be archived or deleted (depending on which you chose).