Light bulb moment!
Our issue was that we were including a target tag in the link to the external site, therefore no returning link was triggered. As this is a site which we do not control, we cannot add a return link to their site.
Now that we open in the same window, it works when you return to our site as advertised. However, the challenge with this approach will to have users actually click the back button a whole bunch of times in order to return to our site and achieve their award.
Unless I’m missing something, that is.