Stroke play challenges, issued individually after the round, should be transmitted to your friend by mail, including a link starting his turn of that round on the same course. Once he finishes, both of you should get a mail showing a comparative scorecard, enabling you to determine the "winner".
Unfortunately, this feature has been out of work for quite a few players. For me, it ceased some eight months ago. From discussions with "Customer Service" and observation of other mails which I still get, I suspect that there is a fault in their mail system blocking some mails for me.
I have to say, unfortunately, that my experience here as told me not to believe in any "promises and hope" raised. I have to live without challenge mails, without tournament notifications, without mails concerning me as a CC owner.
It's a pain in the proverbial!
On a different note, I never understood the CTTH challenges. "abc challenges the world with an xyz score" - how to react on this challenge?