These two verses conclude the opening instruction against visible acts of piety. The entire section is summarized in verse 4, not just verse 3. Thus verse 4 is the express conclusion that comes from the discussion of those who act upon the public stage to receive their rewards of men. The public is rewarded by the public, the private is rewarded by God.
The focus of verse 3 is to emphasize the private nature of the alms. Not only should we not act out our piety on the stage of men, we should do them with purity of heart and singleness of purpose. In the ancient world the connection between the hands was not simply one that recognized that we have two of them, but that we have a duality in us. The left represented evil and the right good. The English word sinister comes from the Latin word for left. There are recorded occasions when certain rabbis would eat or drink only with the right hand, ostensibly to indicate the purity of their actions. (John Lightfoot. A Commentary on the New Testament from the Talmiud and Hebraica. Hendrickson Publishers, 1989, 2:141-2).
In verse 3 it is assumed that the right hand is acting. The left, the one symbolic of evil, is not to know what the right hand is doing. Of course God always knows, but we are to do our pious actions in a way that God will, but not even the symbolic evil one will know.
Textual: There are no changes from the Matthean text.