Not too long ago the waiter at dinner put the wrong bottle of wine on our tab. Things were a bit chaotic at one point and we got the other table's wine on our bill. It was ~$30 different in price in my favor. I didn't hesitate at all in pointing out the mistake to the waiter and I'd do it again in a heartbeat.

In the OP's case it is not particularly clear what exactly happened during the original call. It sounds like they called the hotel, not the program, so the audit trail is somewhat stilted. I'd call it in and point out that the points aren't mine. You may not get to keep them but I don't think it is at all vague in terms of right/wrong. If the original call was to the program office and they let the points stay then the points are yours.

I'm also not sure what the difference is between this case and finding $200 cash in a wallet. If that's what the points are worth and that's what the cash is worth what's the difference? You may not know exactly where to return them to but you know that they aren't yours and you know that there is a way to work towards getting them to the correct home. You don't have to complete the return (assuming you ultimately cannot) but moving in that direction is the right way to go.