We're talking about a fairly small number of rocks scattered across an enormous surface. On the Moon it's even worse because the Earth rocks would simply be lying on top and amongst other rocks. There is no possibility to identify such things from orbit since the rock fragments, after impact, would typically be smaller than could be resolved by an orbital camera and proper identification involves detailed mineralogical and isotopic analyses that cannot be done remotely.
We can, however, be quite certain that Earth rocks have landed on the Moon, and Mars, and many other planetary bodies in our Solar System. We have conclusive evidence of meteorites on Earth that have come from Mars, the Moon, and Mercury. We know this because of their distinctive mineralogical and isotopic characteristics. For example, we have been able to extract trace amounts of atmospheric gases from bubbles within rocks suspected to have come from Mars and we found that they were a very precise match for the atmospheric composition of Mars. Given those facts, and given the fact that simulations of impacts and evolution of the orbits of impact ejecta from Earth should eventually cause a significant fraction of such objects to impact the Moon, Mars, and other planets I think it's a virtual certainty that they have done so.