Imagine you were living with circa 1800 AD technology, and were looking for evidence of another civilization with circa 2014 technology. Keep in mind that this 200 year difference is nothing compared to the difference between modern technology and the technology of a race capable of building a Dyson sphere.
The existence of the advanced civilisation would be obvious to us because they'd be in our villages raping our women. So maybe aliens wouldn't be doing precisely that, but if they are anything like us they would be curious and hungry for resources.
I think the it is significant that the only debris found on the lunar surface was put there by humans. Any sort of exploration of our solar system would have left debris, garbage, broken vehicles, etc. And if somebody invested in a Dyson sphere only 7 light years away, they would be keeping an eye on us for sure.