You can check the battery status of Garmin HRM devices by going to Sensors > HR-XXXXX > About, and scrolling to the last entry. Is this data not present for the Scosche? I took a peek at the ANT+ Heart Rate Sensor profile, and it doesn't document a data page for battery status (common page 82), so chances are good that the data isn't being sent. There is a 'cumulative operating time' field that must be sent and is supposed to reset when the battery is replaced. This could be used to get the number of seconds (rounded to nearest multiple of 2) since the battery was replaced.
I don't have a Scosche to play with, so I'm not a good candidate to do this.
Thanks for taking the time to reply Travis. I checked the sensor settings as you suggested and, despite all other fields being populated, the one field that isn't is battery power! Perhaps something they'll address in a firmware update.
Interestingly, their iPhone app shows battery power though that's Bluetooth not Ant+
