Albert Barnes on Matthew 6:3-4

Let not thy left hand know, etc. This is a proverbial expression, signifying that the action should be done as secretly as possible. The Hebrews often attribute actions to members which properly belong to persons. The encouragement for doing this is, that it will be pleasing to God; that he will see the act, however secret it may be, and will openly reward it. If the reward is not greater in this life, it will be in the life to come. In multitudes of cases, however, alms given to the poor are "lent to the Lord," (Prov 19:17) and will be repaid in this life. Rarely, perhaps never, has it been found that the man who is liberal to the poor, has ever suffered by it in his worldly circumstances.