Very fine scotch brite pad and wd-40 is what we use to clean a #4 satin finish which is what grilles normally are. And yes unfinished stainless will rust, #4 satin finish if rusting is more surface related and generally what is on the surface.

To dissuade Shelby you may wish to try one of these. Scares the bejeezus out of our (stupid, fearless) cats and guests alike.

Here is a link that might be useful: Motion activated spray can

A low tec solution is moth balls. I used to sprinkle moth balls around a rose bush in my garden that was a particular favorite of a neighborhood cat. A mesh bag full of moth balls hung on the grill may deter Shelby the cat.

First, I'd see if a replacement door set is available and order it while the grill is still new. Then stash it somewhere safe until the problem is solved.

Mothballs are pretty good. I've had luck with them.

Is the grill situated so that you can put a little fence around it? I'm thinking dog exercise pen because they're easy open-shut. A cat could scale it of course but it's not the type of thing they'd go over unless they had to. If you could find a cheap used one or borrow one, it might be worth trying.

But no matter how much you block it, you may find that nothing can stop the malice of a cat. I love cats too but when one gets an evil quirk, it can be impossible to cure.

Cat pee is about the worst stuff out there and I would not hold off on the chemicals and hot hot water. If you do get it clean, wrap it with yards of Saran wrap so it can't be hit again.

"And can stainless rust??? Somehow, I thought not. Could the rust be -- horrors -- calcified cat pee or something?"

Note the name, stainLESS.

It is not stainNONE.

Depending on grade it can still rust, and chloride (chlorine ions) is especially corrosive to many grades of stainless (and attacks all of them to some degree).
Use a stainless steel scrubber or non-woven abrasive (Scotch-Brite or similar) to clean the metal.

You likely will then have to adjust the surface finish (polished or brushed) to match the rest of the material.

Stainless that has been welded also loses a good bit of corrosion resistance unless it is correctly heat treated and passivated after welding (a rare and expensive thing in consumer goods).

I know it probably won't help the stainless look better, but you may want to clean it with an enzyme cleaner- Nature's Miracle, is one of many. Cat pee is the worst, I can smell it anywhere.

I can't help with your cleanup, but I sympathize.

Do you let your cats outside? Does your city have a leash law that applies to cats? Maybe you can get your neighbor to keep Shelby in the house.

Our neighbors had a tree destroyed by their neighbor's cat. They saw the cat scratch the bark all around the young tree until it was completely ringed, which killed the tree. The cat owner's insurance paid for a new tree (but the replacement was much smaller than the original). Pet owners are responsible for the damage their pets cause. Just a thought.

Our problem was am raccoon who kept marking and leaving turds on our deck. We cleaned the deck and put new stain on it and so far, Ricky is leaving us alone- but sometimes we hear them at night in out "tree house" bedroom (the maple branches extend over towards the bedroom and when you look outside, you feel like you are in a treehouse). A raccoon fight at night right close to the house is really loud!

We also attract every neighborhood cat as my DH feeds the birds and they are looking for dinner. Very annoying and wish people would keep their cats inside or controlled outside adventures.

If you get your grill cleaned off, I would have a serious talk with the owner- complete with videos.

BTW- one spring I opened our grill and let out a big scream and then thought I imagined what I saw - but no, I opened it up and there was Mickey staring at me wondering why I was intruding on her winter home! We had a brief discussion and she agreed to vacate the premises without a peep! LOL

Cats won't spray where they either have an alternate form of marking their territory (scratching post), or where they feed. I would fix the problem before I cleaned the grill.

It's unusual (but not unheard of) for a female cat to spray like that. They sometimes do it to attract a mate so I am hoping that at least she has been spayed! There are several products on the market that can be used to curb the cat's desire to spray, but it really is a difficult problem to cure especially once it becomes set behavior.

Do they sell a cover for the grill? Maybe that is the best way to go for now. It might encourage her to go pee elsewhere.

If you can't get your neighbor to control the cat, I would call animal control in your town. As others have said, your neighbor is liable for the damage. Good fences make good neighbors!

Duh!! A grill cover! How in heaven's name did I not think of that?

Okay, have ordered spray can gizmo and hung mothballs pending arrival. After that, one more pee and the grill cover comes from Amazon, and even though I dislike having to uncover every time I want to cook, it is an excellent idea. I do have Nature's Miracle on hand -- the cat kind -- and tomorrow I am going out with a Scotch Bright, some rubber gloves, and a bucket of very hot water.

And you know, as crazy as it seems, I think I will ask about putting back a set of new doors if these don't come VERY clean. It's a brand new Weber Summit so should be easily available. I am hoping what I'm seeing is crystalized urine in the crack between door and frame, and I can get it out.

I will have to say, our neighbors have been as responsible as they can be without putting the cat down, and I could not bear that. I would rather buy a new grill. The last time Shelby's mom talked about it, she wrung her hands and literally burst into tears. They love her, but at some point past kittenhood, she just went nuts. She pees all over the house in this vicious, in-your-face kind of way. So they built her a nice, electrically heated house in the garage, where they shut her up at night. The whole family walks the neighborhood looking for her when she runs away -- which is pretty much daily. If Shelby were mine, I'd medicate her with some Pamelor for the aggression, but my suggestion didn't get traction. She IS spayed. It is just the strangest situation.

Only one of our four cats goes out, and only with my husband, 80% of the time on a leash. Our cat has tried to befriend Shelby, but she is very territorial and thinks our yard is her territory. Last time my husband tried to break up the hissy fit, he grabbed the wrong cat out of the shrubbery and got nailed. Ever seen a white, carefully-starched button-down covered in blood? I thought he'd cut his hand off.

Sigh. She is such a pretty cat, too.

Well, excited by all these helpful ideas -- and seeing rain in Monday's forecast -- I forged ahead. Great success! Millworkman, I owe you. That WD40 worked miracles like no cleaner had. After that, it took a lot of elbow grease, a plastic scraper, a Scotch Brite, and a bucket of scalding water mixed with Spic-n-Span, but all the really vile stuff round the door edges came off!! And I think most of the stains. Might still be some shadows left when it dries. Too cold and cloudy now to be sure.

I didn't damage the finish too much, either. If I really looked, I could see a hint of where I'd really, really scrubbed. We shall know more when the sun comes out, but I think you'll have to "know where to look" to see the damage. I'm okay with that. It's a grill.

I also had the notion of tenting some extra-splintery firewood across the doors, then spraying them liberally with Cat-Away repellant. Maybe it will ward her off for a day or two. When the spray-racket gizmo arrives, I will take the firewood down.

Thank you all again so much.

Something uncomfortable to step on might discourage her, or it might just make her change targets. They often hate double-stick tape and that 1/2-inch egg-crate plastic gridding sold for lights.

When female cats start spraying, they are almost as bad as un-neutered toms for persisting.

Yup. Had a female that sprayed. 'Had' being the operative word.

Dis GUSting.

Wishing you success after all of that work!

Good luck!

I approve of your nice attitude towards neighbors and psycho kitties. :)

I have had amazing luck with Bayes Stainless Cleaner. I have tried just about everything and found it to be the best.

Highly recommend a motion activated sprayer to keep the cat away.

Well, the firewood is holding the lines of battle so far. The motion sprayer wouldn't work. I couldn't get the parts together even after a hour on the phone w/the mfg. Sigh. In the sun, you can tell the grill has been over-scrubbed. I am going to have to go smooth it out by buffing down all the doors. Thanks for the sympathy!

Didn't someone post a video on here of a VERY loud, motion-activated system for a cat on the counter that scared the bejeesus out of it? That would be very effective, but might take a bit of effort to rig up.

I had a cat peeing on my front door a few years ago and I used our motion-activated Halloween "scary sounds" device. Seemed to work. Heard it go off once in the night and that was it.

Thanks, ella socal. I got the SSScat from Amazon. Supposed to spray water with a hissing sound, but for the life of me I could not get it to work. I like the Halloween idea. And it would be weather proof. Even the SSCat looked like it was for indoor use only. I am going to go to eBay and see what might be lingering from Halloween.