If the rubber cut is large, replace even if the inner casing is fine
I just realized I'm really stupid today.
I have a Schwalbe Marathon Plus Tour Hs404 700x40c and it is quite resistant, allowing me to do a bit of gravel in between roads on my touring.
On May 2021, I got my first flat on it. It was a perfectly shaped pointed stone, with a very flat base which managed to make it through. I had ridden a Schwalbe of the same type for about 2 years by then, and I know it was a rare occurrence.
After I removed the stone, it left a cut of about 6mm on the exterior rubber. But the inner casing looked fine, and unless I pressed it with my hand, the cut was not very visible, so I decided to continue riding it.
Then today on August 2021 I was doing some other repair, and I noticed that a another stone was stuck in the exact same place! Luckily this one didn't puncture.
But this drove the message home. So soon after the flat, another stone was stuck in there, and I know that tire is quite resistant.
If there's a significant cut on the rubber, replace the tire, obviously. This one was likely a close call for me getting another flat in the middle of nowhere and spoiling a ride or worse.
The stone before I removed it:
The hole when I'm pushing it open:
The inner casing, apparently intact:
Criggie mentioned in the comments that it should be possible to repair in some cases, which hadn't crossed my mind, so I had a look for it.
The following video from GCN actually explains how to repair even the inner casing by sewing it, but inner casing repair is not a job that would be worth my time on my 35 dollar tires.
They then repair the rubber cut with a product known as "SHOE GOO", which was originally intended to keep shoes of skateboarders going longer, and is readily available.
I ended up buying this one labelled "Shoe Goo II" (it has to be better than the original one, right??): https://www.amazon.co.uk/Shoe-Goo-Crystal-Permanent-Adhesive/dp/B08P5V9GQV I haven't tested the patched tire on the road yet, but the result seems solid and might actually prevent further stones from sticking in.
Here's how the result looks like, with me pressing to open the cut, and it just did not open. I didn't do a perfect job, added a bit too much of it I think, but I'm guessing the excess will just be scrapped off while riding and shouldn't be an issue.