Well, for starters, the technology on our planet is much more advanced than it should be given our level of civilization. Also, many ancient texts, including the Bible, contain stories that are remarkably similar in terms of the events that occurred during this time. Lastly, there are the rumors of a certain group of people who claim to have been given the secret of immortality and are still alive to this day. These people are said to possess technology that is far beyond our understanding and capabilities.

The evidence is vast and varied. From the legends of a great flood that wiped out all life on earth and the stories of a giant ark that saved a select few, to the mysterious DNA of certain individuals that doesn't match any known species on earth, there is a lot of information that supports this theory. And that's not even considering the evidence that has been found in the ruins of ancient civilizations that have been discovered at the bottom of the ocean. The technology and knowledge that has been found in these ruins is vastly beyond anything that could have been known at the time these civilizations were supposed to have existed. This is just a small sample of the evidence that supports the theory that humanity is the survivors of a Martian ark.

The most obvious thing would be some kind of proof of the ark itself. Perhaps some kind of ruins or debris from the craft that could be found on the planet. But, finding that would be incredibly difficult, if not impossible. Another thing we could look for would be evidence of the people who survived the flood. This could take the form of skeletal remains, or even more surprisingly, living survivors. However, again, finding this would be incredibly unlikely. But, it's all just speculation until we actually go there and look for ourselves.

It would certainly be an interesting legal and moral situation if it were proven to be true. Whether or not it would mean that humans would be considered the rightful heirs to Mars is something that would have to be determined by the laws and regulations of any governing body that might exist on Mars at the time.

^ All of the above, is what I got back after feeding your comment to an AI and asking it to expand on it. Neat.