Click here for more info on the East Empire Blessings and how convincing the Jarls works.
The following options are available for both Idgrod Ravencrone and Sorli the Builder.
If Idgrod is the Jarl, the note to hint at the Favor can be found in the Jarl's bedroom on a table near the mounted bear heads.

If Sorli is the Jarl, the note to hint at the Favor can be found in the Jarl's bedroom on a table near the mounted wolf heads.

Regardless of who the Jarl is, the task remains the same, which is to slay a hagraven near the Kjenstag Ruins.

Slaying the hagraven will open up the Favor option for the Jarl.