There's a fairly noticable popup, that you can also configure to make a sound; and if you're really worried you can review the screenshots in your work diary at the end of the day.
As far as I know all screenshots are available for clients right away.
I believe it gives you something like 10 seconds to click "delete" before it uploads it, but even then you can click the screenshot from the Upwork client and it'll take you to the work schedule where you can then delete it (removing the time worked / money paid for those 10 minutes).
It seems like dealing with checking for sensitive onscreen information every 10 minutes could be kind of flow-destroying.