If OP is working for a top 10, travel contracts aren't negotiated by the "travel desk" but by specialists reporting to the CFO. Marriott isn't going to discuss anything with OP nor will OP even get to anyone at Marriott who could discuss this if he could.

As others note, interfering in your employer's negotiations with third parties is a good way to make some powerful enemies very quickly.

There are any number of reasons why your employer has chosen to give its business to another chain. If you are planning on sticking with your current employer, I would switch to its preferred chain.