That page says and seems to indicate that there are options and I would assume that choosing "skip" or ignore, the nagging should stop. Assuming you don't actually want to update for some reason.
Regrettably, the operative word there is "seems." (I am reminded of the still funny line from an early episode of the TV program "Everybody loves Raymond" where Debra, his wife-to-be, says, on meeting Ray's parents, "They seem nice," and he replies, "Yes, they seem nice.") I have not seen a Windows version of Quicken in a long time, but at the Quicken forum, Windows users complaining about this issue say that the option provided in the pop-up to check "Skip" and/or "Do not remind again" is ignored. Checked or not, the pop-up reappears each time Quicken is opened. In the Mac version that I use, an option to choose "Skip" is not even offered.
chscag, here is more than you probably want to know: When I first switched from Windows to Mac, I purchased Quicken Essentials for Mac (QEM). It was a weak app, but okay for my purposes (I use Quicken only to balance a checkbook). QEM was replaced by Quicken for Mac when Intuit sold it to ... someone. I don't know the details, but at the time I (like thousands, millions of others) received a pleasant email message explaining how great life was going to be in the new neighborhood. I purchased the new Quicken from the new guy, and it stank. Really stank. I got a refund, waved goodbye, and purchased Checkbook Pro. I like it. Then, the new owner of Quicken sent me (and thousands, millions of others) an email message, apologized for the first roll-out, said everything had been fixed, and please come back. Well, it sounded like they meant it, so I went back, and that's where I am now. Old habits die hard.
However, I still have Checkbook Pro on my Mac, I still like it, and now, as regards Quicken, I am sorely tempted to, as you put it so succinctly, burn it, rip it up, shred it, and then throw it away.