I've taken to just closing Evernote completely when I'm not using it ... and favoring other tools I have when Evernote is not the obvious best choice.
This approach makes the tool less useful, but also far less annoying.
There's a management concept that's been around for decades -- "Management by exception". The idea is that reporting should highlight things out of the ordinary; you do not bother people with information that's by definition non-actionable. (It's why 'error messages' are frequently used, but 'health messages' less so.) Evernote designers appear to be unfamiliar with the concept, or their marketeers have overridden those with better judgement to get 'in our faces' more to promote product mindshare.
It's not a good long-term strategy. The marketeers have forgotten that one pissed-off user can ruin the word-of-mouth from a bunch of happy users -- and they are creating a bunch of pissed-off users here. It's self-defeating.