I think this explains it - found on Bkool blog....
"For the time being, this connection [Bkool & Garmin accounts] will only show workouts from Garmin Connect and send them to your Bkool profile. It will not synchronise your activities on Bkool to your Garmin account however we are not ruling this possibility out for a future update".
7 years and no fix from Garmin.
AFAIK, Garmin does not develop any interfaces for 3rd party services. Garmin already has an API that 3rd party services can use. The 3rd party needs to acquire the access to the API and develop their own interface. The access to the the API for writing back to Garmin is restricted more than the read-only API. It requires a certification process (to avoid spoiling Garmin's database with bad data), and possibly also some license fees. That's the true reason why the number of 3rd party apps writing back to Garmin is much lower than those who use the easier accessible read-only API.
There is not much Garmin can do for you here. You have to speak to the 3rd party service and persuade them that the additional hurdle of acquiring the full access to Garmin's API is worth of it.