I have seen a few cases where older Android Wear devices may get stuck and data will not synchronize between the mobile and wearable device. If you run into this scenario, the first thing to do is to try and re-pair the device. If this fails, you can also use the resync option built into the companion app.

However, if this fails to fix things, there is one final set of steps you can do to completely clear out all saved data.

1. Factory reset the watch: Settings ... Reset device
2. On your phone: Settings ... Apps ... Google Play services
3. Click on clear cache
4. Click on manage space
5. Manage wearable storage ... Clear now
6. Under total data used by Google Play services ... Clear all data
7. Reboot the phone
8. Try to pair the phone with the watch again

These instructions were written on a Nexus device running stock Android. If you have a device from another manufacturer, some of the steps to get to these options might be slightly different.