Forward them that email from the CP saying there are no training contracts, and tell them "your lawyer" has advised you you don't owe them anything. If they persist, find an actual lawyer to write a letter telling them to f-off.

You're fine, they're just trying to shake you down.

For further reading, go do research on "liquidated damages vs. penalties" in contracts. This is obviously a "penalty" they whipped up out of nowhere.