> We should be wary of bringing Martian microbes back to Earth, because they may find our environment too hospitable and end up invasive species.
They could even already have invaded in the past, and we descended of them[1]. Earth as Mars ancient lifeboat[2].
Yes, that is perfectly possible. There could be some transfer, but there is a scenario where Martian microbes breed on Earth and have no natural controls. An Australia type scenario on a planetary scale.