is there a way to fix a bad studio recording?

I'm afraid that if this is a legitimate CD release, they're all going to be like it. It's not necessarily the studio's fault at all - it's the way a lot of 'popular' material is 'mastered' - basically to make it as loud as possible so that it stands out on the radio, or whatever. And even if you could remove it, there's no way you can restore the peaks on that much clipping without reducing the overall level of the track significantly.

Mind you, it's not that clever a recording, and clearly somebody has had to do some work to it before it was released. If you look on the spectral display at the point where 16kHz is (near the top), you'll notice that there's a slightly darker band right across the track. This means that somebody's run a filter across the whole thing. A few years ago I discovered (the hard way) that if you have something like an iPad or other medium-sized display anywhere near an open mic, the backlight power generator is perfectly capable of generating and radiating interference at around that frequency - in just the same way that the line oscillators in old-style TVs did. And people tend to take them into studios... Generally it doesn't become apparent until much later, often at the mastering stage, and it's virtually impossible to remove this invisibly (the reason is technical and boring, and relates to the way digital filters have to work).

Often, your best bet is to get somebody to make a recording of the track from the vinyl release using good equipment. They have to take a lot more care with clipping and peaks on this, or it simply won't track correctly on the player. If it still sounds crap after that, then somebody blew it completely at the mastering stage, and there's nothing that can be done except complaining like stink to the record label, and getting them to remix it properly. Personally I think you should do that anyway!