We're aware of the situation and are monitoring it. Good news first: that particular user won't be bothering us for a while.
At least not from that IP address, but I know for a fact they've used multiple IP addresses in the past. We've taken out their IP addresses.
Anonymous users are very hard to moderate and some of their actions can indeed be a nuisance. There are a couple of approaches possible, none of them great.
rene's answer details one of them: a spam/vandalism flag on a suggested edit. This is the right tool if the edit is destructive, it's the wrong tool for poor edits. However, considering the limited tools we have, some consider it an acceptable tool versus anonymous users. While we're investigating the possibilities, no review suspensions will be handed out for using this option on anonymous users. Please stick to the proper tools with registered users. Even if it would've been the correct tool, if the goal is to take-out repeat offenders with this you'd have to know it's a repeat offender at the time of rejecting. Collaborating about the moderation of the site in chat has been done with great effect in the past in The 2nd Monitor, don't hesitate to do it again. If need be, new rooms can be started. They're free-of-charge.
If the edits are truly nonsense and the user has no other participation of value on the site, the user can be destroyed. Destroying a user for spam will feed their IP into SpamRam and has the benefit that it can be done years after the fact. Doing this for poor edits is still not the right approach, but can be an option for repeat offenders without contributions of value.
Another approach is to limit the action of all unregistered users. Sites can petition the staff to limit the privileges to disallow answers, disallow suggested-edits, etc. It's actually fairly easy to get implemented and has been used with great success to stop unscrupulous actors in the past on other Stack Exchange sites. However, we're not going to take this approach unless there's support for it from the community. It's not a nuclear option, but it comes close. Personally I'm in favour (the amount of garbage edits we get from anonymous users is percentage-wise high and the amount of effort it takes to create an account is small) but this is still not an autocracy. If you think there would be enough people in favour, feel free to start a meta question suggesting it. In an emergency situation, we could temporarily instate this somewhat rapidly.
Rejecting a specific edit permanently is not an option enabled by the system, nor would it be a viable approach. I'd very much like the option to disable suggest-edit privileges per IP like we can do per user, but AFAIK there's no support for that by the system.