Golfshot Pro members can score directly from the Apple Watch. From the main distances screen, swipe left and use the digital crown on the side of the Watch to adjust your score and putts. Your scores will be reflected on your iPhone during your round.
If you have pro and do not see the score screen, this could be related to settings. Launch the Golfshot app > Settings > GPS, Scoring, Caddie > Turn Auto-Advance to Next Hole OFF.
If you are playing without your iPhone, just turn Bluetooth back on at the end of the round and your scores will sync to your iPhone.
You can turn off scoring in the Golfshot app settings > GPS, Scoring, Caddie.