Dave here from the Guru Team :)
If you would like to remove that from the Quick View page you can certainly do so! If you go from your Admin to Online Store > Themes > Customise Theme > Product Quick View. From there if you uncheck the box that says 'Show Availability' and then save. From there that will no longer be displayed for you :)
All the Best,
Dave | Shopify
I came across this question trying to figure out how to ADD this feature. I have gone to the location you said to turn it off and it seems that my theme doesn't have this option. Is there a way to get it without revamping my entire site? An app maybe? I've been searching for an app for a while but can't seem to find one that gives the "one left" on the main product pages (Like with all the tops I carry).