Of course, you've got to recognize that Sirach is an Old Testament book, so it must be included in that proper context. An example of another OT citation of this includes:
Daniel 4:24 (RSV) Therefore, O king, take my advice; atone for your sins by good deeds, and for your misdeeds by kindness to the poor; then your prosperity will be long.
As an FYI, there is also this reference:
Prov 16:6 (RSV) By loyalty and faithfulness iniquity is atoned for, and by the fear of the LORD a man avoids evil. (note: St John Chrysostom translated this, in his 9th homily on Hebrews, as “By alms-giving and acts of faithfulness sins are purged away.” He was referring to the Septuagint when making that statement -- included only as an FYI)
And then, of course, there is a famous New Testament quotation of Our Lord,
Luke 11:37-41 (RSV) While he was speaking, a Pharisee asked him to dine with him; so he went in and sat at table. The Pharisee was astonished to see that he did not first wash before dinner. And the Lord said to him, "Now you Pharisees cleanse the outside of the cup and of the dish, but inside you are full of extortion and wickedness. You fools! Did not he who made the outside make the inside also? But give for alms those things which are within; and behold, everything is clean for you.
I cite the above not to, in any way, deny the completeness or efficacy of the sacrifice of Christ on Calvary, but to point out that the quote from Sirach that you cited was not hardly unique in the Scriptures.
My King James says in Daniel 4:27
27Wherefore, O king, let my counsel be acceptable unto thee, and break off thy sins by righteousness, and thine iniquities by shewing mercy to the poor; if it may be a lengthening of thy tranquillity.
Righteousness gets turned into ‘good deeds’.
Prov 16:6
6By mercy and truth iniquity is purged: and by the fear of the LORD men depart from evil.
The question here is WHOSE mercy and truth? I would say that those belong to the Lord, nothing that we can do as men.
And FYI, a homily or commentary do not carry scriptural weight.
Luke 11:37-41
37And as he spake, a certain Pharisee besought him to dine with him: and he went in, and sat down to meat.
38And when the Pharisee saw it, he marvelled that he had not first washed before dinner.
39And the Lord said unto him, Now do ye Pharisees make clean the outside of the cup and the platter; but your inward part is full of ravening and wickedness.
40Ye fools, did not he that made that which is without make that which is within also?
41But rather give alms of such things as ye have; and, behold, all things are clean unto you.
41 does NOT say - Give alms and this will amke YOU cclean, but that all things will be clean FOR you.
Giving alms does not provide atonement, there is NO salvation through works, lest any man boast.