Hmmmm,that's strange. Someone asked about the same problem not more than a couple days ago. Several ideas were presented. Maybe you could look for the thread since it was so recent.

It looks quite small. Are there several more?

You don’t show the rest of the wainscoting...but it appears as if it would be less obtrusive if the whole center was covered with some type of decorative metal screen ...rather than a sectioned .... trimmed ...recessed ...cubby

Coordination of the trades falls to the GC. Either the HVAC duct was located with no consideration of the wainscoting or the wainscoting was a change to the original plans and specs after HVAC rough in.

If it's a supply, I'd suggest installing those in the floor. If it's a return, I'd aim to get it out of a formal area and certainly out of wainscoting.

New home build, return vent. Had no input in the Hvac and location of vents, etc. I have sent photos of what I would like it to look like. It can definitely be aesthetically more pleasing to the eye. It is a shame the home buyer has to micromanage building their own home.

"Someone asked about the same problem not more than a couple days ago. Several ideas were presented."

That would be the same D Macky. Why did you start TWO new threads 4 days later on the exact same thing? Continue on your first thread by answering questions, dismissing ideas, or updating thoughts or bringing new information and respect the free time that commenters put into this forum.

BTW there's no way to fix this except by tearing out the wainscot, drywall, and probable rework of studs and sheetmetal.

www.houzz.com/discussions/6128850/help-with-wainscoting-around-intake-vent

www.houzz.com/discussions/6130766/trim-work-around-intake-vent