The back-radiation from the atmosphere is comparatively much less total solar energy, but oceans are good at absorbing and storing thermal back-radiation reflected back off the greenhouse gas rich atmosphere into the ocean. This is a tiny amount of the total heat Earth gets from sunlight, and the increase of this radiation due to greenhouse gas is a fraction of one percent of solar energy, but it adds up.

One way to explain this is that 85 degree air will warm 80 degree water. That's a thermodynamic law. It just takes a while and because the heat capacity and density of water is much greater, it takes about 4 liters of air to give 1 degree back to warm 1 cc of water 1 degree. But despite the inefficiency, warmer air still transfers heat into colder water. It takes many decades, perhaps centuries, for the oceans to catch up to the warming air, but air, however inefficiently, does warm the oceans.

The quirk in this, is that the oceans, despite warming much more slowly than the air, are still absorbing over 90% of the trapped heat added by the increase in greenhouse gas. It's a matter of scale. Oceans warm slowly because they're enormous and always circulating and it takes much more energy to war them, but they also absorb most of the heat, for the same reason, they're very good at holding heat. Slow to heat up, but also, slow to cool down. That's why bodies of water often feel warm when you go swimming at night.

I should probably add something about increased evaporation in higher air temperature, which effectively cools the oceans and surface air, but also increases the greenhouse effect with an increase in water vapor, but running those numbers is a bit over my pay-grade. The greater efect is the one mentioned above.

The cause of this super greenhouse effect at the surface is the rapid increase in the lower-troposphere humidity with SST; that of the column is due to a combination of increase in humidity in the entire column and increase in the lapse rate within the lower troposphere. The increase in the vertical distribution of humidity far exceeds that which can be attributed to the temperature dependence of saturation vapor pressure; that is, the tropospheric relative humidity is larger in convective regions.

https://en.wikipedia.org/wiki/Thermal_insulation

"Thermal insulation provides a region of insulation in which thermal conduction is reduced or thermal radiation is reflected rather than absorbed by the lower-temperature body."

As you can see, it is without doubt very clearly stated, that preventing heat loss, or retaining heat, is done in the exact opposite way to what the theory of global warming claims. Absorption is what you want to avoid to prevent heat loss. There is a lot of things in the warming science-camp that indicate a lack of physics education in their field of science. Actually, every single argument in the greenhouse theory is a head-on violation of known, proven 100% consensus physics.

So, first of all, according to proven physics, it is highly unlikely that there is a warming climate at all. Secondly, the ocean cannot warm, if the amount of heat from the sun doesn´t increase. And we know that it doesn´t.