There is a way, but it requires a bit of manual work.
Since the only way to use Garmin Connect is to have one of their devices, record any activity (it doesn’t have to be cycling) with your Garmin device and sync it to Garmin Connect. Then export that activity to a tcx file.
Open the tcx file from an editor (notepad, notepad++, …) and locate the xml section ‘creator’, which for me looks something like this:
<Creator xsi:type="Device_t">
<Name>xx-Your device-xx</Name>
<UnitId>xx-Your unit serial number-xx</UnitId>
</Creator>
The section may be longer or shorter for your device. In any case, save it somewhere as you will need it.
Go to Trainer Day and Export the TD activity you want to import into Garmin Connect as a tcx file.
Open the exported tcx from an editor (notepad, notepad++, …) and after the ‘Lap’ section (after the </Lap> tag) add the Creator section you saved.
Save the modified tcx file and import it into Garmin Connect.
Activity imported this way will count towards Garmin Challenges.
I’m a bit of a developer, so I automated these steps with a little app I made myself, but anyhow - it takes only a few minutes to do everything manually.
Garmin’s limitation is pretty strange, since the only way to have Garmin Connect is to have a Garmin device!? So why is there a limit?