You need to:
- Do the skinless god's questline (Salt Plains, Flooded Town, Salt Plains) so that Oscar inherits the purifying salt.
- Do 3 things to get Oscar's affection up (like getting him the nice clothes at the tailor, then visiting Storm's home and then P's family home), which leads to Pedro giving Oscar a feather when they go to the cemetery.
Oscar will purify the tree while holding the feather, which will partially burn it — thus it becomes an "ashen" feather.