I know many would think or say it shouldn't happen or that a really great UX team doesn't allow it to happen, but the true is it happens a lot (even though successful teams!). I just would like to hear from other experiences, how did you manage to overcome these kind of situation.
That's all there is to it. Every feature has to have a purpose. Clearly state the reason behind this terrible thing marketing did and identify a way to measure it's impact. If it fails the test, it has to go. That's just good business.
Choose the right metrics
Kerry Rodden at Google Ventures developed the HEART framework to assist in determining your experience metrics. These don't have to be touchy feely things focused on smiles and rainbows — hard business numbers are acceptable too.
Making things right
No feature should ever be launched without first having a clearly stated purpose and associated measurement. On the other hand, it happens. When you have a chance to reevaluate, select your metrics and watch the trend for a while (or pull historical data) to find out if it was really a mistake or not.
First of all, there is a need to prove it does have a negative influence on usability. So yes, test or study is due. It might uncover marketing team was right or that nobody was right.
Then there is a question on what exactly you mean by "what to do with this". If this is about go/no go, it should be a decision of the Product Owner. If the marketing is overpowering politically, there is an option to go with their design but install analytics and later demonstrate the numbers to disprove them and suggest a change driven by the UX.
From my experience, every feature implemented on the site has to have some form of KPI (key performance index) or score assigned to it. The KPI/score can be used to measure & track, the usefulness of the feature users, Or the value that it bring to the site / business (SEO improvement, convergence, user/customer engagement).
Have periodic review of the features on the site to determine what needs needs to be added, what to needs to be improved, what need to be switched-off.
Work with the team that introduced the feature to understand their underlying goal. Collaborate with them to conduct user research to determine whether the feature meets their underlying goal, as well as what its impact is on the user experience. Collaborate with them to identify solutions to the problems that are uncovered in the user research and work with the engineering team to prioritize improvements based on your research.
Definitely test test test and film the users reactions to the feature. A film of a user completely dismissing a feature will win over any decision maker...
The other answers are correct: Test.
But what are you testing for? If just for usability, you might end up with a perfectly usable system that doesn't support users' actual tasks. You could have a usable system that supports marketing tasks instead.
So I'd suggest also doing user research early in the process, when the UX team can have some influence on what's being designed and built. You want to discover what your audience's pain points are, what they need to accomplish, and what tasks they're trying to accomplish as they use your system. These findings are, in my experience, usually at odds with what the marketing department wants.
Then when you test prototypes of the system, test not only usability, but test whether this helps people do the real things they need to do. (Otherwise, you might end up using tasks in your usability tests like "Can the user find Promotional Landing Page X?" when no human would ever do that.)
Evgenia Grinblo has a great talk about this subject here: https://www.youtube.com/watch?v=lR-KCmGQeFo