This is about the claimed “saturation” of CO2 absorption by the atmosphere (where “saturation” here refers to the idea that a relatively small amount of CO2 will block almost all of the radiation in its spectral absorption band and so that further increases will have little or no effect – which is actually the exact opposite of what saturation really is).
This argument was made by Angstrom and co-workers in 1901 on the basis of experiments measuring the CO2 absorption spectrum for radiation shone along a tube containing the same amount of CO2 as an atmospheric column of the same cross section. Its main flaw is due to the fact that the gas in the tube is fully mixed and exchanges heat energy with its surroundings (through the sides of the tube) and so the experiment neglects the effect of re-radiation upwards from heated gas in the lower atmosphere.
Unlike the gas in the tube, an atmospheric layer that is almost totally opaque to the absorbed frequencies will not in fact completely eliminate them from the Earth’s emitted radiation. This is because when heated up by absorbing that radiation, the layer in question radiates a full thermal spectrum from both its top and bottom surfaces and that from the top includes a portion that could be absorbed by a second such layer – and so on. So the number of such layers matters and increasing CO2 does lead to a slightly increased surface temperature (but the effect of successive layers diminishes so that the overall expected warming is only (approximately) logarithmic, with successive doublings of the CO2 concentration each giving roughly the same small temperature increase). But even just a “small” increase can have a big environmental effect – especially if it is unusually rapid in geological terms and relative to the capacity of species (and economies) to adapt.