9 “That your alms may be in secret.” What else is meant by “in secret,” but just in a good conscience, which cannot be shown to human eyes, nor revealed by words? Since, indeed, the mass of men tell many lies. And therefore, if the right hand acts inwardly in secret, all outward things, which are visible and temporal, belong to the left hand. Let your alms, therefore, be in your own consciousness, where many do alms by their good intention, even if they have no money or anything else which is to be bestowed on one who is needy.
But many give alms outwardly, and not inwardly, who either from ambition, or for the sake of some temporal object, wish to appear merciful, in whom the left hand only is to be reckoned as working. Others again hold, as it were, a middle place between the two; so that, with a design which is directed Godward, they do their alms, and yet there insinuates itself into this excellent wish also some desire after praise, or after a perishable and temporal object of some sort or other.
But our Lord much more strongly prohibits the left hand alone being at work in us, when He even forbids its being mixed up with the works of the right hand: that is to say, that we are not only to beware of doing alms from the desire of temporal objects alone; but that in this work we are not even to have regard to God in such a way as that there should be mingled up or united therewith the grasping after outward advantages. For the question under discussion is the cleansing of the heart, which, unless it be single, will not be clean.
But how will it be single, if it serves two masters, and does not purge its vision by the striving after eternal things alone, but clouds it by the love of mortal and perishable things as well? “Let your alms,” therefore, “be in secret; and your Father, who sees in secret, shall reward you.” Altogether most righteously and most truly. For if you expect a reward from Him who is the only Searcher of the conscience, let conscience itself suffice you for meriting a reward. Many Latin copies have it thus, “And your Father who sees in secret shall reward you openly;” but because we have not found the word “openly” in the Greek copies, which are earlier, we have not thought that anything was to be said about it.
Source: Our Lord's Sermon on the Mount (New Advent)