Only the the exceptionally uninformed try to deny the existence of the greenhouse effect itself. I don't think most of them do that at all, though people that does don't seem to be that uncommon either. The basics of the greenhouse effect have been understood for nearly two hundred years now, if Fourier's mostly qualitative description counts.
Anyway, turning off the greenhouse effect would cool global mean temperatures by a lot, down to its effective blackblody temperature, which one can estimate by Stefan–Boltzmann to be 254K = -19°C. Of course, such a thing would also drastically raise Earth's bond albedo from about 0.306 as the Earth becomes a snowball, so the temperature would ultimately fall much, much lower than that. To fix this, extreme changes in the Earth's energy budget, e.g. higher solar output (maybe some extreme geothermal heat or whatever if we're pulling a ROB anyway).
Furthermore, without the greenhouse effect, the atmospheric lapse rate would be completely messed up, with (at least) greatly inhibited convection and ultimately a more uniform tropospheric temperature. I'm not at all sure what that would do to weather and climate, other than render it completely unrecognisable, even if mean surface temperature stays the same by some means.
A necessary ingredient for the greenhouse effect is appropriate absorption spectrum of atmospheric molecules, specifically that the excited modes that change the electric dipole have frequencies in the infrared. And one can't change that without affecting basic chemistry of those elements, so a pasted-on ROB exception would be revealed for the magic that it is.
The most conceptually straightforward way to counter CO₂ contribution specifically (which is small compared to total greenhouse effect) may be to introduce another gas for an anti-greenhouse effect, perhaps in the stratosphere, i.e. something absorptive in the visible and transparent in the infrared. Though the actual climate is complicated and has many various feedback loops that I'm sure a ROB could manage to do so basically undetectably from us for a long time, with exactly what's happening to counter it staying a long-term puzzle.