There is faint remnants of a bitcoin logo on it and the words 'paper wallet' and the name of the website from which it came printed down the right hand side.
Chances are this website should NOT be trusted (anymore). Many once trusted paper wallet generators turned into a scam later on, by creating pre-determined instead of random private keys.
If it is bitcoinpaperwallet(dot)com it depends when the paper wallet was created. This site used and still uses a clever folding scheme for their paper wallet print templates.
After the original creator Canton Becker of this website sold it approx. by the end of 2018, the new owner(s) now scam you. Any paper wallet created on this current scam website uses predeterministic private keys known to the website owner even when the site pretends that you generate some sort of entropy (you don't!). Any more or less decent amount of coins will vanish from recently created paper wallets from this scam website! DO NOT USE IT, if that's not yet clear enough!
@easternklaas: you should check if the public address of the paper wallet which should also be printed on the paper wallet does still hold any coins. If it doesn't there's not much left to discuss here, except for the interesting ethical topic. As block explorers I recommend mempool.space or bitcoinexplorer.org, but others like btc.bitaps.com or blockchair.com are OK, too.
Not entirely sure if you did that already...
... From there, I did a crash course in paper wallets, and figured out how to identify the balance of the wallet,..
BTW, nice to see that you do your own research.
Secondly, I would verify the private key does indeed lead to the address on the wallet. I would do this on an airgapped computer as mentioned above by Loyce. I would never enter the private key on an internet connected computer due to the risk of theft.
Airgapped is not enough, it should stay airgapped forever until erased. Use TAILS in offline-mode as it forgets any data, unless you use persistant storage. An offline copy of bitaddress.org script in TAILS should be OK to check everything needed (use Walletdetails on that page, works offline).
Thirdly, I would make up a back up of the wallet. If it is already damaged as you say, then I wouldn't want to risk being responsible for damaging it further beyond recovery, especially if it is the only way for someone to access their life savings.
...
Lastly, I would post the public address here to increase the chance of the owner finding it.
A safe usually digital copy is not an easy task. Smartphones are not appropriate for this. If the paper wallet is still readable why bother. If you can't 100% trust any device used for the copy process, you put the paper wallet to risk of theft by others.
Yep, I would post the public address, too.
So at least there will be a chance that the owner will recognize his paper, card or or some other sign if he sees this topic.
They all look the same
But I can’t immediately figure out how the owner will confirm his right to this 0.6 BTC if he has neither backups nor access to any information that allows him to confirm.
Be creative: "Before laminating it, I wrote the current date in blue ink on the paper. I can verify the handwriting is mine."
By posting an image, you make it easier for scammers to describe the paper wallet.
Indeed, it's not uncommon there's some handwriting on the paper wallet, hopefully it wasn't with water soluble ink and some or all of it is still preserved and visible.
@easternklaas should not post any physical details of this paper wallet anymore for that reason as already said by others.