As a child the good thing about having a puppy was that the nastier bits of my mum's cooking could be slipped under the table and be eaten, fat and gristle seem to have been an important part of of our diet. Puppies under the table is perhaps the image we have from last Sunday's OF Gospel. It's is a nice image, but actually of course it is not meant to be nice, it is supposed to shock us.
Jews in the Old Testament often used dogs as an image of apostasy or of idol worshiping Gentiles, it is an image Jesus takes directly from scripture. Dogs are unclean, a source defilement. Jesus wasn't sent to the 'dogs' but to the children of the Israel. The women makes the image even more horrific by speaking of the dogs 'under the table'. It presumably is supposed to summon up images of those vanquished kings who had their fingers and toes cut off who were made to beg for food under or around the table of the victor. The woman in order to gain a favour from Our Lord s willing to abase herself, to admit her absolute dependence on him, she is dog sniffing for favours. The EF Gospel for last Sunday was the Publican in the Temple, who goes home justified because he abases himself in the Temple, it is the same idea.
The difference of course is the idea of food, of begging for food. I don't know if I am making too much of this, I tend to see all references to food, certainly in the Gospels as pointing to the Holy Eucharist; are we supposed to be like those begging kings made powerless without our toes, or more importantly, fingers, begging at the Lord's table, waiting , for those scraps which elsewhere in the Gospels are collected with great care? Presumably without fingers they either eat from the floor with food thrown down from the dais or lie my dog when I was being particularly kind had food placed in his mouth.
I must admit I am open to the idea that possibly as sign of intimacy Jesus actually placed the Eucharist in the mouths of his disciples. I remember an Indian archbishop who stayed with me briefly and scandalised me and the husbands of the local Indian community by insisting on placing sweet pastries directly into the mouths of their young and pretty wives, the ugly or older women helped themselves or received them in their hands. It was obviously a gesture of great intimacy, interestingly he wasn't too happy with doing the same during Mass with the Holy Eucharist. The reception of food placed directly into the mouth is in other context than Mass is one of extraordinary intimacy, eating without using our hands is a sign of absolute dependency or trust. Eating whilst kneeling is sign of complete subjugation, this is what the Canaanite does in order to receive a scrap or a crumb of mercy from the Lord.