All you have to do is look at the graphs to see
CO2 back radiation is a minor bit player when talking about the ocean.
For example, increased well - mixed CO2 and water vapor decrease the rate of heat loss
through back radiation.
The major one looks to be additional latent heat provided by evaporation which is being caused
additional back radiation and the warmer water column.
Although back radiation is real, it does not play a major role in the greenhouse effect — mostly because of the lapse rate, which is mostly set by convection.