Two items:
1) In the options, you can enable end-of-game messages which - for strokeplay - include the invitation of WGT friends to compete based on your score. They will get a mail with a link to a game under matching conditions, and a comparative scorecard will be sent to both players after the second game is completed. This one works and may provide some fun.
2) The OP is talking about CTTH. There and via WGT, you can somehow initiate a challenge to beat your result, but this is only published in your activities. So, nobody will personally receive the challenge, and there's no way to compare the two CTTH scores via WGT.
As I said, the purpose of this item has been a mystery to me for all my time on the site. To me, it looks like some idea never completed, like the CC bank.