How do I wipe a microSD card that I can't write to?

You may consider following the legal route instead of the technological route. Probably the company in question has some sort of privacy statement - check it out on their website and get a written conformation (email with a person's name and function should be enough) that your data will be kept private. After that, send your microSD card, with a note physically attached to it stating that you explicitly exercise your right that your data is being handled according to the privacy statement.

Another option is to explain your concern to the manufacturer and agree (with the manufacturer) to the following route (before execution of it): make a picture of your microSD card, showing that it is in perfect physical condition. Take a picture of today's newspaper with it to date it. Print a log of your failed deletion of the file - preferably dated after you took the picture of the card. After that, take a hammer and smash a nail through your microSD card and send it all (photo, print and destroyed card) back to the manufacturer.

Finally, if you're not willing to take the risk, take your losses and buy a new one. For compensation you might want to consider buying a lottery ticket too and try your luck there. :-)