The easiest way to do "counter-geoengineering" would be simply lifting emissions limits, carbon taxes, etc., at least until the point where the economy is thoroughly decarbonized and we don't need to create pressure to emit less GHG, because right now emitting is cheaper than not emitting.

I think right now, any country willing to invest resources to fix our shared mess would at worst be met with some grumbling about unknown risks, but otherwise mostly with a "sure, knock yourself out", and possibly a silently muttered "thanks".

Counter-geoengineering is an interesting concept and long-term problem, but I don't think there are many powerful countries that don't want the planet to cool.