Your rights are provided for under contract
law. What you describe is a contract law question. As a party to the contract, you have the right to enforce the contract.
Under contract law, when two parties negotiate a contract, both are bound by the terms of the contract. But this assumes there is a "meeting of the minds" over the terms. If there is no meeting of the minds, then that can be grounds to void the contract
For example, A and B negotiate the purchase of a "bat", A thinks he is purchasing an object to strike a ball with. B is selling his pet fruit bat. In such a case, there is no contract, since the parties do not agree on what is sold.
Another example: A thinks he is buying a wooden bat, as he is allergic to aluminum. B is selling his aluminum softball slugger and advertised the item as "softball bat for sale". I this case, it is more complex, since B advertised an item that correctly described what was sold, and A had a limitation but did not specify it during the negotiations? It may well be that A is stuck with the bat.
In your case, it may be you can argue that you did not have a valid contract if you can show that what you agreed on was not what was delivered.
To do so, you would have to prove that the "standard" desk height is less than what they delivered. If you can prove that? If you can prove that there is a standard desk height, and you negotiated that and what they delivered varied from that? Then you can sue to recover the cost to fix the problem.
You will have the burden of proof
...so you will need to provide evidence of what is industry standard. But if you can do so? And you can prove that what they gave you is not industry standard? THen you can void the contract based on that.