This just started happening to me today -- this not really a solution but may be helpful to some: I use Evernote on Mac/iPhone exclusively w/o Google integration set up. No problem for years - Evernote added a little favicon to the left of Drive links pasted directly in as mentioned above, but they weren't visible when I added display text to the link and there wasn't the whole bubble thing. Anyway, I logged into Evernote web and viewed the note to check something and viola... synced back to my desktop and bubbles!
I tried testing with a few test notes and this pattern *seems* to hold: I can create/edit a note with drive links just fine on my Mac; as soon as I edit the note on web (viewing on web may be fine, but haven't tested extensively), the synced note on Desktop is all bubbly.
That said, it *seems* I can delete the original text on Mac, insert new links and they appear normal (and continue to appear normal after sync). And the behavior does not happen on new notes I create. So for whatever reason it appears I'm experiencing a somewhat different problem than JodyHealth.com is.
My current solve: "Never use Evernote web" ... which, ok.