Using alcohol and abrasives are the absolute WORST way to remove permanent marker from vinyl. This bad advice needs to be stamped out all over the internet.
A far superior way: 1. Get a dry-erase marker and write over the permanent marker. 2: Get a damp cloth. 3: Wipe it away. 4: Repeat as needed.
Nail varnish remover removes sharpie inks off most things .. however try a place that will not be seen before having a go at the main floor , it may just melt the vinyl.
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