Thread Matter devices talk via thread to the Matter controller/fabric they are joined to.
Then a Thread Border Router would act as the man in the middle for other Matter controllers that are not on that thread fabric to communicate with the thread device.
So if you paired the thread Matter device to Alexa, any of the Alexas that are TBRs would be the man in the middle (Thread Border Router) to let external systems communicate/use the thread device on their thread fabric.
It's all shown graphically in this post. I recommend it:
