There's a simple explanation for hard-to-erase magstripes; they're the newer "high coercivity" type.
Old-style low coercivity magstripes are essentially the same material as is used for cheap ferrite cassette tape; they have a coercivity of only about 300 Oersteds. That means a 300 Gauss field is enough to wipe them. You can easily get that from a plain ferrite magnet, or an electromagnet you can make in ten minutes with some wire and a nail and a lantern battery.
Floppy disks score 720 Oersteds, higher coercivity tapes (DAT, 8mm video tape...) can score as much as 1400-odd Oersteds, and high coercivity magstripes are as tough as hard drive platters, in the few-thousand-Oersted range. Some high coercivity stripes apparently manage as much as 4000 Oersteds, though I think ISO Standard 7811 only specifies 3000. Magstripes are, of course, easier to wipe than a drive platter with the same coercivity, because you can lay a magnet right down on top of a magstripe; they don't have an aluminium casing around them like a hard drive.
My giant rare earth truncated pyramid fridge magnet has a real live 7000 Gauss field strength at its small end, which is way more than is needed to wipe any magstripe ever made. The part I grabbed is the big end, but that's quite likely to still manage better than 4000 Gauss.
Ok, maybe an immense magnet could do it. These are neat numbers to find. It turns out modern mag stripes are much harder to damage than the ones we had years ago.