This question already has an answer here:
New users already have a reminder to accept an answer on their question. So I don't see the need in general for this post-answer badgering, even if it is intended to be genuine constructive help (which it almost always isn't). To me it seems like little more than rep greed, especially on a site like StackOverflow where such a reminder comes within 10-20 minutes of posting the answer, and when the comment is clearly intended for the OP to accept the commenter's answer. To me it feels like pressuring the OP to accept their answer before a better answer has a chance to come along (or, as others have put it, rep-whoring).
I know we've talked in the past about how users should decide when and how to provide such comments, but that deals with the behavior itself. I'm asking about how we should treat the comments after they've come - I'm not sure whether I should send the commenter to the meta question I just linked, flag the comment, or ignore it. Ignoring it doesn't feel right, but saying something in the open might not seem genuine in cases where I have a competing answer.
EDIT I'd like to add something to consider here: the case where a user makes it seem like further discussion or clarification of an answer hinges on an up-vote/accept first. A couple of examples I culled recently, but I don't want to call out the user here (they're both from the same user, on different posts, in response to questions trying to clarify their answer):
consider up-voting my answer if you found it useful first.
up-vote my answer if you found it helpful first.