If you put in a support ticket, you may be able to get them to sell you the original replacement pads for the cooler. I think it's about $10. I like Kingpin KPx paste, but the others mentioned are good too.
 
The only issue is that I don't think they have the putty anymore that comes on a lot of these cards. You could try some gap filler putty available online. Something like this one, but I haven't used that one personally, so I'm not sure how well it'll work. It looks like it'd be viscous enough, but you'd have to try it. You can try to search the forums here, just make sure you change the settings at the bottom of the page from "30 days" to "from the beginning".
 
Edit: Here's a thread discussing pad sizes if you want to buy your own from Gelid or something. they do say in the thread that the 3080ti sizes are the same as the 3080 sizes. There's also this page from EVGA that has them all, specifically the XC3 hybrid.