It's usually a good idea to use lights or red filters on underwater cameras to try to recreate colours at depth more accurately. However, this isn't always possible, and, especially in research situations, sometimes less gear is better!
However there is a quick way to adjust colours to get a much more realistic final video. The white balance tool is found in most video editing suites, and allows you to identify a known "white" area in your video (usually using a crosshair or eyedropper icon); the software then corrects all the other colours relative to that white area. You only need to do it once and the new colour profile is implemented across the entire clip, with the usual result being a restoration of the red colours, and less of a blue/green tinge.
The video below is a split screen edit of a clip recorded with a GoPro (without a red filter) on the front of a Spot X ROV. By simply finding a spot in the clip with a known “white” area we can colour correct the whole clip. If you dive or survey in areas with clean sand, then taking the white balance reference point from there is going to yield a great result. You can see in the high shots the green tinge is taken out of the water, and in the close shots, the encrusting algae and invertebrates have a lot of their natural red colours restored.
In terms of post-processing editing tools, this one probably gets you the biggest improvement from the smallest investment in time, and well worth a try next time you edit your underwater video.