First of all, entropy can refer to either, depending on context. Your context was ambiguous, but that's no one's fault. Sure, let's use your definition.
Your idea about the upper levels of the atmosphere mixing with the lower levels is utter hogwash. What does that even mean? The defining characteristic of the upper levels of the atmosphere is that the air is thinner. If those upper levels came down here, they would be just as thick as the levels extant, due to the atmospheric pressure.
There are underlying laws of physics that govern our world (and, of course, our observable universe). Those laws still apply, even through the increase of entropy. "Randomness" doesn't mean "crazy things can happen", it means "unordered distribution of matter".
If the air gets random enough, then it will kill everything on the planet (think upper layers of the atmosphere mixing with those down here). Of course, that is not likely to happen, given the amount of disorganization you or I is likely to cause by picking up some trash, but why take the chance when you can sit at home and be lazy? Also, entropy refers to an increase in randomness (randomization?), not a loss in energy.
You're confusing your goals. Our goal is not to reduce the entropy of our biosphere; it's to remove pollutants. The increase of entropy does not detract from our goal. Further, we have an infinite (for all intents and purposes) source of energy coming into the system: i.e. the Sun. So entropy is a non-issue, because any energy lost can be steadily regained.
I am assuming that anything anyone does here on earth will not affect the order of anything more than what they are working on and the surfaces they come in contact with in the process. If this is the case, any energy expended cleaning up the environment will be more than negated due to the increase in the entropy of the air around them.