Can the people whose votes were removed sue the state (or whoever if in charge)?
In theory, maybe. In reality, what would they be asking for? They won't get their votes reinstated. They won't collect money damages, because they can't prove that they suffered any. We have no good metric for how much a vote is worth (and in reality, if we tried to make such a metric, the amount would almost certainly be tiny).
But this just goes to the absurdity of Griffin's argument. The voters did not in any way fuck up, because even if they knew there were issues, they couldn't have done anything about them. The people who would have both standing and resources to sue are the campaigns. And if Griffin had brought this suit in 2023, we wouldn't be so contemptuous of it. I mean, it might still be a bad-faith, mostly bullshit argument, but at least it wouldn't be trying to change the rules after the game was played. But they didn't.
IIRC, one of these cases was brought to the PA Supreme Court and was dismissed on laches -- which is a principle that says you can't win a case, even if your position is meritorious, if you have unreasonably delayed to the detriment of other parties. One classic example of this can occur in the patent context. Let's say you have a patent on something -- I don't know, let's say, you have a patent on something related to a smart phone. Then you notice someone who you think is ripping off your patent. The proper thing to do is to tell them to stop, and then bring suit. But instead of suing, you sit back and do nothing until that other company sells like a million of those phones -- and then you jump in and say, ah you've breached my patent. Now I have control over your whole business. A court could say, "nah, you should have brought that claim when it was ripe, instead of waiting for the other person to first build up a huge pot of money that you want to take."
Same thing here. The proper time to bring the lawsuit was before the election. Then the problem can be fixed, and people can go vote. But if the problem was fixed, then those voters would vote as normal -- and since your goal is to disenfranchise people on the other side, that's not what you want. You want them to vote with "illegal" procedures and then reap a windfall by invalidating their votes. Waiting until after the election should be strictly prohibited and dismissed under laches (and there are several other grounds for denying Griffin's challenge, both constitutional and federal statutory, but laches is in some way the most straightforward).