Well, since mining is a race and messages from mars arrive last, that eliminates that as a valid place to be mining -- all else being equal.

But for using the bitcoin blockchain, there's essentially no difference between using it on Mars versus on earth. Sure, it take you an hour and a half to see your transaction confirm (versus one hour for six confirmations here on earth), but other than that, there's not much of a difference.

As far as using a second layer (e.g., lighting network) or sidechain on mars, sure -- some of those would likely need mars-local versions to be useful in the same way. But even from mars, I could do a bitcoin spend on earth's Lightning network, if I am willing to use a node on earth -- it would just take 30+ minutes before I would know if the transaction succeeded.