It runs locally in your browser, without sending your training data to any servers.
Unless you choose to save it to Google Drive.
If you choose to host the model with Google, they get a copy of your weights, but they still don't see your training data.
Or you can host it yourself with tensorflow.js
And you can also download everything in a zip file, training data and weights, and Google never sees any of it.
If you want the source, it's here -> https://github.com/googlecreativelab/teachablemachine-commun...
https://github.com/googlecreativelab/teachable-machine-v1