First, we have to assume there is a nearby extraterrestrial civilization that is inquisitive enough to invest the resources into building interstellar probes.
They first identified Earth as inhabited in telescopic surveys, then they wanted to know what lives here. Given the extreme physics of interstellar travel, answering that question is no small expense.
Secondly, these probes are built purely for data collection and beaming findings to their home planet. They are the mechanical equivalent of Lewis & Clark, with the intelligence to self-reprogram their mission depending on what they discover.
A probe's mission is not to plant the flag of Zork on top of the U.S. Capitol, or make direct contact such as: "Greetings from the Zeta Reticulans. how are you?"
In a paper published in the 1960s, Carl Sagan, using the Drake Equation, statistically estimated that Earth might be visited every few tens of thousands of years by an extraterrestrial civilization.
If this is a reasonable estimate, then what evidence might have been left behind? (And pull-eeze - it's not the Great Pyramids, not the Nazca lines and not Stonehenge!)
For starters, the probe might self-destruct after reconnoitering the solar system and transmitting its findings back to its builders. It would be "retired" simply for the sake of not polluting our system with evidence of alien technology. For biological quarantine, NASA crashed its Galileo orbiter into Jupiter, and that is the ultimate fate of the Cassini probe at the end of its mission to Saturn.
But could you program an artificially intelligent machine to commit suicide? It simply might change its mind.
Given all the expense to get the probe here, its builders would strive to make it immortal through self-repair, if not replication. This is embodied in the popular idea of a Von Neumann machine.
The probe would have to find a place to park and collect resources for self repair (but not a stop at Radio Shack). It may be instructed to do a re-reconnoiter of our solar system periodically and go into hibernation for long intervals. (No, it wouldn't need to tap into our power grid as alleged in several goofy UFO stories. Who needs energy from a fossil fuel-dependent medieval planet?)
The visitor could park in a solar orbit. If the probe detected artificial electromagnetic transmissions from Earth, it might go into stealth mode to avoid detection and capture. After all, it couldn't collect much data if it were snagged and put on display at the National Air and Space Museum in Washington D.C.
Even if visitors to our solar system were sloppy, with one or more probes leaving debris on asteroids or even planets, the artifacts would be pretty difficult for us to detect.
NASA's Lunar Reconnaissance Orbiter (LRO) has photographed our lunar artifacts, such as the Surveyor 6, shown here. But we knew what we were looking at. Even the shadow from a black alien monolith on the moon might get overlooked as just another tall boulder.
To get attention, a piece of space junk from an alien probe would have to be big and morphologically peculiar, or have an odd spectral signature or albedo.
One example is an LRO image of the Soviet Lunokhod 2 rover that landed on the moon in 1973. It stands out brightly against the regolith and has parallel wheel tracks.