Is there any sin in recording calls – with the owner's permission – for the purpose of referring back to important calls, while deleting others without listening to them?

There is no harm in recording calls if explicit permission is given, or if it is known that no harm will result from it. Otherwise, permission must be sought due to the potential harms that could arise. One should refrain from recording anything for which the owner's consent to record is not known. As for what is known that its owners consent to its recording, there is no harm in recording it and letting those who can benefit from it hear it.