I just had a computer that attempted to update from Win10 1703 to Win10 1709. After several failed attempts and automatic rollbacks, the computer finally ended up with a BSOD that I could not recover. I ended up doing a clean install of Win10 from an ISO
(win install disk). Of course, everything was wiped and I won't get into how upset I am about the whole automatic update thing here.
My point is that I had the green arrows showing up for the first time ever on any computer I've had. The root cause for me was that One Cloud was set by default to backup several things. I did not set this at install nor was I given a choice during the install
process.
Fruitlessnoodle's reply
was the answer to my case. At the bottom of windows in the taskbar over on the right side, in the tray area, is where the one drive icon is located. In my case, I had to hover my pointer over the up arrow to show hidden icons. The white "cloud' symbol is
the One Drive. I right clicked the cloud to get to the menu that has settings. Clicking settings opens a box with several tabs to change what happens with the One Drive storage.
The autosave tab allows you save to "this computer only" for several items. This turns off automatic saving in the cloud and then you won't have automatic syncing across devices form One Drive and you won't have green check marks on your desktop icons.
If you choose to use this feature in the future just turn it back on.
And that is the mystery of the green checkboxes (at least for me).