I've done this! You can see them with the naked eye quite easily. Just shine a light diagonally at the surface. I wouldn't bother reading them by hand though. You could take a photo of it with a digital camera then post-process it and stick it through mathematica or something.

However you might as well just use a card reader.

I used to hack stored value phone cards back in the very early 1990s. First they had an optical system which was easily circumventable with a torch a knife and some epoxy glue. Then there were the smart card ones which were easy to hack by scratching off the programming voltage pad on the card.

I got to the later mag strip cards like this and couldn't be bothered any more.