I doubt that any race, after having developed the ability to travel among the stars, will leave heaps of rubbish. They may leave a message but it would have to be a physical object as asteroid and micro-meteroid impacts would over time wipe out any pictographs scraped into the lunar surface.
The only logical thing they might do is to bury an object that could only be fashioned by an intelligent species but that would not give any information... they would have no idea if Earth dwellers would be peaceful or warlike and would not want to leave an "Encyclopedia Galactica" or anything that would help a warlike species leave its solar system. Perhaps something as simple as a plaque made from diamond or titanium and engraved with the relative positions of the nearest 15 pulsars at that time, thus allowing us to determine the approximate time they left it.
It would be most unwise to leave probes or scientific instruments as that may contain a technology unknown to the Earth which might inadvertently advance a weapons program or other technology that we "are not ready for" at the time we discover it.
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