There's no such thing as bad publicity; how about in science? If the original paper is proved wrong, how on earth could the original authors get any job and respect from their academic colleagues?
If it turns out they’re wrong, then they will likely do a follow up paper that explains what their mistakes were. No biggy. It’s just a couple of preprints, after all, and it’s widely believed that it was pushed out without all of the authors’ consent in the first place. It won’t leave them with lasting reputational damage from their peers, though it may place slightly more scrutiny on their outputs at a later point.
They may get ridicule from the people who took their paper at face value without noting the informality of the format, the incomplete studies performed on the sample, the almost-clear methodology etc. But those people aren’t scientists - all of the scientists who have discussed this have assumed from day one that it is likely an error, and perhaps toyed around in case their assumption is wrong.
To have reputational damage, they’d need to refuse to retract their work, refuse to elaborate further, claim they invented room temperature superconductors without sufficient proof, then attack anyone who questions them.
Reputation matters, so don't commit fraud and don't try to trick others. That is the sort of thing you won't be recovering from. But being wrong is fine, even if you truly believe(d) that you are right. Note that this whole saga was not started on the timetable of the people that have the most at stake. I'm hoping they are right, I'm fearing they are wrong and if it turns out that they were wrong then I hope that they will not be dissuaded by that and that they and many others will continue the search. There are a lot of things that came out of materials science in the last two decades that we'd have never had if not for people searching for them. Not all of those searches will pan out, that's pretty much a given. Think of it as sifting for gold in a mountain of junk. For every piece of gold there are piles and piles of junk. And sometimes stuff that looks very much like gold, but ultimately isn't. That should not affect the reputation of the seekers. They are either going to try again, or maybe they'll give up. But what others think of them doesn't matter all that much.
And even if the research is incorrect LK99 is still going to be a useful addition to science.
Everyone just needs to take a deep breath and put down the pitchforks.