Most people I know with dogs try to train them not to beg at the table.
In my daughter's house, the dogs are well behaved and stand to the side while we eat: but the kids had to learn that if they accidentally drop their food on the floor, it's fair game for the dogs!
I voted for the second option, but if a dog is not too demanding, I can imagine thinking it is cute, while not in the least bit tempted to give any food away.