Are you asking why we never found a small number of Earth rocks scattered over the entire surface of the Moon during a period of only a few hours total of lunar exploration? The answer should be obvious.

To be fair...the surface of Earth's moon has been much more extensive than just physical lunar surface exploration.

It's also a fair question, have we seen evidence from this on our moon? And if not is it really because of the limited exploration or some other factors?

Thank you josefresco!

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.

I agree that it could be due to limited lunar exploration. Having said that, my concern or thoughts is that, why we limited our exploration mission to moon? I have been looking for answers for a long time.

I'm not sure what you mean. It ended up costing about a billion dollars per person to send someone to the Moon. And those are incremental costs. Few people thought that the costs of the moon program justified the expense of keeping it running.