Since the locale is Mars, the life is probably (but not definitely) a different lineage than our own. Mars has very different qualities compared with the Earth: An organism adapted to live there might do terribly on the Earth. But, organisms might be adapted to Mars of a different era, and be adapted to a more similar environment.
Except for the fact that it is there, as the place is now. So, unless you are going to postulate that the thing has gone dormant and can manage to remain viable for... centuries? Millennia? Eons? Then it is adapted for the current conditions on Mars. And that's *very* different from here, and even more different from the environment inside our animals or plants.
I am not kidding about oxygen being a poison. Oxygen *really* likes to burn things. If you don't have machinery to divert it to useful purpose, it combines with random molecules in your organism instead, and that organism dies.
Mars of a different era? Mars probably hasn't been warm and wet for a billion years or more. When Mars dried up, we didn't have multi-cellular organisms on Earth yet! You don't cling to your adaptation to an old environment *that* long. Evolution would have taken them to adapt to their current environment, not stalled them still looking for something from a billion years ago.
Or there might be that odd chance that the organism can handle an Earth environment.
There is always a chance, yes.
If I change this around: Let's say a Rover scratches its way to a subsurface layer which is teeming with life. No alien structures, just an unknown but definite collection of biota. Should we plan on sending people to study it before sending probes to do a careful study beforehand?
Nope. But, I think almost everyone active in the conversation is saying we go with probes first. We can set all the biological issues aside, though, as this decision is made by economics and engineering - we can probably do several rounds of developing and sending probes before we'd be ready to send a human. There's no reason to *stop* sending probes before the humans get there.
Also, note I mentioned upthread that the real risk is not in Mars contaminating us, but us contaminating Mars. Biological samples from mars will become very expensive trash if they get contaminated with Earthly organisms. And the same thing that will protect use from contaminating samples will keep the samples from contaminating us.