The Scythe's ability triggers even if something other than the damage dealt by the equipped creature causes the creature to be put into a graveyard that turn.

Scythe of the Wretched needs to equip your creature when the other creature goes to the graveyard for the ability to trigger, but it doesn't matter whether the Scythe equipped your creature when the damage was actually dealt.

If the card isn't a creature when it comes back onto the battlefield, then Scythe of the Wretched won't move onto it.