For the last few months I've been importing activities from Strava (tcx files), but the last few times I've tried to do this, it it says that my file was not accepted by the system.
In fact, all you need to do is opening the TCX file with Notepad and remove the leading white space at the very beginning of the file. There must be no white space at all in front the tag <?xml version="1.0" encoding="UTF-8"?>. Once you remove the leading white space, the file imports just fine to Garmin Connect.
You should also ask Strava to fix that error, because it violates the XML standards, hence it is not surprising Garmin Connect refuses reading it.
I recorded them on my phone, using the MyETraining app (the app for my trainer) using power, speed, cadence, etc. data transmitted from the trainer and heart rate from my Garmin watch. Then I uploaded from that app to Strava and then exported from Strava to Garmin Connect.