If you're a Potterhead, you know that the Dursleys are some of the worst people in the entire franchise, only surpassed by the pink dread that is Dolores Umbridge. They are the epitome of judgmental assholes, and they took great pleasure in tormenting Harry for being different. But there is one small detail from the books that made me think they perhaps cared about him at least a tiny bit.
After Harry left Privet Drive and started at Hogwarts the Dursleys pretty much ignored him for the majority of the year with the exception of the summer breaks. They wanted nothing to do with magic and wizards and instead focused their energy on prying on the neighbors. However, there were three instances throughout the books where the Dursleys actually sent Harry a Christmas gift. In the first book they sent Harry a toothpick, in the second one he received a 50-pence coin and in the fourth book they treated him to a single tissue. Of course these gifts are absolute crap, but they bring up some interesting questions.
How did they send them?
Little is known as to how Muggles can send letters and packages to Hogwarts. We know it is done on a few occasions, such as the Dursley presents, but J.K. Rowling never really told us how it happens. She does leave one clue in the books though. There's a scene from Petunia's childhood where she is speaking to her sister Lily (Harry's mother). Lily is a witch and is going to Hogwarts, something Petunia seems to have conflicting thoughts about. She sent a letter to Dumbledore, asking if perhaps there was any way she could attend the school as well. Lily found out about it, and so did Snape.
"Severus saw the envelope, and he couldn't believe a Muggle could have contacted Hogwarts, that's all! He says there must be wizards working undercover in the postal service who take care of –"
"'Apparently wizards poke their noses in everywhere!' said Petunia, now as pale as she had been flushed."
If Snape was correct, it means that in order for the Dursleys to send Harry a Christmas gift they had to willingly get involved with the wizarding community, albeit indirectly. Considering the fact that they despised everything about magic, this shows an odd sense of dedication from their side.
Why did they send them?
It seems strange for the Dursleys to send Harry these incredibly cheap Christmas gifts, it's an awful lot of effort they have to go through just to send him a toothpick. It's not really explained why they do it, but one theory is that it's connected to the protection spell Dumbledore performed on their house in Privet Drive, the one that ensures Harry can't be attacked there as long as he can call the place a home. Usually you do receive Christmas gifts from those back home, so perhaps that was part of the deal. If that's the case however, it doesn't make any sense that they only sent them three times, instead of every year.
Personally I think J.K. Rowling only added these gifts as a joke to emphasize just how horrible the Dursleys were, it's a children's book after all. If this is the case, she rather achieved the opposite. If the Dursleys sent Harry three Christmas gifts, no matter how crappy, without any specific reason, it goes to show that deep down inside they did care for him in their own strange way.
After all, we do know that Petunia cared for her sister Lily, so it's not unlikely that she pulled a Snape and secretly projected that care onto Harry. I'm not saying this redeems the Dursleys of course, they were still terrible people. But it adds some more complexity to Petunia's character, and if there's one thing I'd like to see more of in Harry Potter it's that.
If you're in the mood for a little Dursley throwback, here's the clip from Harry Potter and the Sorcerer's Stone where they do everything they can to avoid Harry getting his Hogwarts acceptance letter.