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What a wonderful question! My Bible search yields a couple of thoughts.
For example, in Hosea 6:5-7 it says: "For I desire mercy, not sacrifice, and acknowledgment of God rather than burnt offerings." And in Matthew 9:12-14: "But go and learn what this means: `I desire mercy, not sacrifice.' For I have not come to call the righteous, but sinners." Since a reference to "the law" usually means a reference to the Old Testament, I believe the Hosea verse is probably the law to which Jesus is referring.
This would then put a whole different twist on this verse from your reluctant reading. The guiltless or blameless would then be those who are sacrificed by the priests on the Sabbath during "worship". Jesus was in the process of rebuking those who had criticized Him for harvesting grains to eat on the Sabbath by pointing out that David entered the temple and ate bread set aside for the priests, and how the priests did not have clean hands either because they continued to condone sacrifice of the guiltless. There is a powerful message here for us as well. How many of our cherished customs and beliefs in church rest upon the acceptance and condemnation of the suffering of others?
This passage also brought to mind more of my favorite verses from Hosea: Hosea 8:13 "They love sacrifice; they sacrifice flesh and eat it; but the Lord has no delight in them. Now he will remember their iniquity, and punish their sins. . .". Also, Hosea 4:6: "My people are destroyed for a lack of knowledge." For me, this underscores that if more people just knew what meat eating did to them and the harm to their own bodies and spirit, they would give it up out of "enlightened self-interest."
Hope this helps.
Your sister in Christ,