being magnetic doesn't mean a steel is
not "stainless", it's an indicator of different types [400 series, not 300], or cold worked, I'd expect those tapes are subject to a high polishing process after cold rolling
I took a load of non-ferrous to the scrapper yesterday and using his strong magnet found some of the thin 'stainless' was magnetic, but he didn't throw it in the ferrous pile, there was a separate bin for martensitic stainless
which info doesn't bring back your dissolved tapes of course

Bill