I know it seems like a silly thing to get emotional about, because Dudley was a jerk for years and something like this of course does not make up for that - but it’s the beginning It’s the begininng of Dudley’s redemption, and it shows that his journey on redemption is a sincere one.
Because Dudley doesn’t really know how to express love. He’s never had to, nor never really particularly desired to before. So he doesn’t know how, but he thinks about what makes people happy - tea makes people happy, right? But the idea of making Harry a cup of tea and bringing it to him is scary, expressing feelings like that, talking about emotions we’re ashamed of is hard enough for the best of us, for Dudley it would be even more so. So he leaves the tea outside Harry’s door, attempting to do one of the few kind acts he understands.
As a metaphor, imagine Dudley had a very limited verbal English vocabulary, and while he wanted to say “I’m sorry” and “Thank you” and “I care about you” and “I hope you have happiness because I see now how much you deserve it”, but he does not know all these words, so all he can say to express himself is “tea”, because he knows that tea makes people happy.
And as Kurt Hummel and Dave Karofsky would say, “Here’s to baby steps.” Because without baby steps, no major change within a single person could ever happen. Redemption and huge positive change within a person can not happen overnight. But they do happen, and they start like this.