We've always played that the "piece" had to have been part of you when you died.
Consider though: Does Disintegrate take your gear as well? This has varied through editions and I honestly can't recall that detail from 5th.
If there's stuff remaining, look through the clothing for a bloodstain. It will be there if the character took any other damage in the fight. Their blood, on their person at the time of their death would qualify, wouldn't it?
As for Reincarnate v Disintegrate: I'm kind of a rules guy. In earlier editions Reincarnate and Resurrection would both create a new body, and the revived person suffered some penalties. True Resurrection restored them to life without penalties.
So, to me, if it says True Res' it means True Res'. (Yeah, I know the "penalties" thing isn't clear or overtly meaningful in 5e and may not be there at all, but it's the fine line that differentiates the spells.)