From Addison Hodges Hart, Taking Jesus at his Word, exploring almsgiving in the Sermon on the Mount:

“The right hand has provided the gift [of charity], but the left hand is kept in the dark. this is a metaphor with a touch of the mystical about it. It means, that in some way, we hide the deed even from ourselves. WE don’t dwell on it, congratulate ourselves over it, but instead move on to other things.”

I should add, these words could easily have come from Kierkegaard’s pen – see his Works of Love.