It's nothing to get nervous over. The servers just are very interested and motivated to make sure you're happy. What they don't want to happen is have you not finish something because you don't like it and go away unsatisfied, but not say anything. Myself, in a regular restaurant, if I'm not happy with something, I'll generally not say anything, because I don't want a big production made over the situation, the manger to come over, and so on. I just won't go back to a restaurant that's not to my liking. I think a lot of people are like that. But that's exactly NOT what the
DCL servers want to happen. They just want you to be happy, and sometimes come off as pushy because they know many people are reluctant to say anything. It's not as if they get a commission from every plate of food they serve. They have no incentive to push more food onto you, other than to keep you happy.
As to how to handle them, in the rare occasion it's been an issue, I've simply said "Don't worry - you've provided excellent service." or even better, "You've provided 5-star service." Then they know that you know how the game is played, and that you're not going to hold it against them, if indeed there's any issue at all other than your being full.