Weird clauses in terms of use are frequently just toilet paper when it actually comes down to enforcing them in court. You can "sue" but you might just win $1 because the judge would find that you have not suffered any monetary damages. You got paid for the item, after all, and "building a relationship with your customers" has no quantifiable and measurable value which can be proven in court, so judges default to one dollar.

There is also the aspect of whether an AI agent has the legal capacity to contract on behalf of Amazon or the buyer, and on whose behalf they contract if they do. I'm not aware of any American cases which have held that AI agents are "agents" (an entity with the legal power to act on behalf of another) within the meaning given to that word under the law of agency. The Civil Resolution Tribunal in British Columbia, Canada, ruled in Moffat v. Air Canada that AI chatbots can bind the organisation who uses them and makes them available to customers. This opinion is not binding precedent, but I think courts worldwide should use it as a template for AI agency powers. If the AI has no power to contract, then the sale is void in its entirety.

I believe Amazon would argue three points:

1. That the AI agent has power to contract, but that the "user" of the AI is the shopper, and Amazon is merely providing the agent for the shopper to use.
2. That if the clause banning AI agents from buying is enforceable, it voids the transaction in its entirety, and thus the seller owes Amazon a refund.
3. That even if the AI had the power to bind Amazon, that the ability to build direct customer relationships has no proven dollar value and thus damages should be limited to nominal amounts (i.e. one dollar).