Serendipity put a bag of magnetic heads for cassette players on the same workbench where I was pruning my wallet out of expired receipts. While laying down some expired subway tickets (here the subway tickets are printed on thin cardboard the size of a credit card, and have a black magnetic stripe glued on a side) seen the cassette heads, and got the idea it might be possible to read the magnetic pulses with an audio cassette player head.
Couldn't resist the temptation and tried. Audio heads give very small signals, but the hard magnetics used for magnetic cards have stronger magnetic fields than audio tapes. I could also try to swipe the magnetic stripe as fast as I can, so the signal might get large enough to capture directly from the heads.
After cutting away the magnetic stripe from the subway ticket (so I can pull-swipe it by hand over a cassette player head, happened to be a mono head) I've got an unexpectedly high signal, in te 10-100mV range!

Kept the cut strip pressed with a finger, and pulled the strip with the other hand as fast as I could, with the scope on single swipe and trigger at 20mV. Why pulled by hand, the magnetic strip increase speed, that's why the increasing amplitude and increasing frequency of the captured signal. After a few tries got a clean strong signal.
I expect nobody would believe that, so took a picture of it and some oscilloscope screen captures, one with the whole swipe, the others with a zoom-in.

Note that some peaks are close together, while other peaks are about twice far apart. Chances are that's a pulse duration encoding. The count of pulses/edges displayed by the oscilloscope didn't work properly with such an irregular signal.
I didn't try to decode the pulses, that would be too laborious. IIRC there are more than one standard for magnetic cards, they have 3-4 tracks, etc. Random example, first search result for magnetic card standard:
https://www.q-card.com/about-us/iso-magnetic-stripe-card-standards/page.aspx?id=1457