Deleting a person should be done in Planning Center People anytime you want to delete that specific person on both platforms. The only exception comes when a person within Notebird has an update or task saved to their profile. If that is the case then their profile is archived in Notebird instead of deleted.
If you want to delete someone ,you can find them directly in Planning Center or use the quick link from Notebird.
Click the Planning Center profile link under the person's name. That will open up their profile in Planning Center
Click the Gear dropdown on the right hand side
Click Delete Profile (follow Planning Center prompts)
For more information, read Planning Center's help document on Inactive vs Deleting