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When they are screening a call, if I push the button to answer the call, the call comes to me immediately.

They used to play back a 10 to 20 second "polite" message that just annoyed everybody.

I don't follow what you mean. You have a call screening program or something?

But I'm not sure what that has to do with the Do Not Call database.

I think "call screening with Google Fi" is some kind of service/feature, which they have enabled.