I don't have personal experience with this but if you google "Jet blue seat" and click on images in the upper right of the search results you will see pictures of the jet blue seats from the front, back, and side.
You can get the same type of pictures for the cares harness by googling "cares harness."
Based on the pictures it looks like the strap *might* interfere with something -- either the tv or the tray drop down tab. As you can see from the pictures there is virtually no (actually a very small) gap between the end of the tv and the start of the tray tab.
Maybe the belt can go under the tray -- i.e. you drop down the tray to put on the belt and then close the tray over it so that the tray remains usable. [Again, this is a guess not actual experience.]