I just do not want it to be a case of money sent wrongly. In the first place, i shouldn't even be cashing out money from some random, unknown source.

Fair point, but unfortunately Coinbase help (https://help.coinbase.com/en/coinbase/trading-and-funding/sending-or-receiving-cryptocurrency/how-do-i-refund-a-digital-currency-transaction) doesn't mention article what to do in this case (unknown sender using on-chain transaction), it only mention return if the sender also Coinbase user.

Since i'm not legal expert, i only can advice you to contact Coinbase support about this problem.