If it wasn't in the original contracts for the equity, they wouldn't be able to claw back.
Fairly obviously, the mechanism can't be in the exit agreement because you didn't sign that yet.
Normally a company has to give you new "consideration" (which is the legal term for something of value) for you to want to sign an exit agreement - otherwise you can just not bother to sign. Usually this is extra compensation. In this case they are saying that they won't exercise some clause in an existing agreement that allows them to claw back.
Per the Vox article, it's not directly in the contract you sign for the equity, it's basically part of the definition of the equity itself (the articles of incorporation of the for-profit company) that OpenAI remains in full control of the equity in this way.
Normally a company has to give you new "consideration" (which is the legal term for something of value) for you to want to sign an exit agreement - otherwise you can just not bother to sign. Usually this is extra compensation. In this case they are saying that they won't exercise some clause in an existing agreement that allows them to claw back.