I typically choose to use my debit card when I'm buying something, in the interest of saving that business a few cents.  However, shady looking messages like the one below don't sit well with me.  Asking "is this a debit card" is a bs question intended to get more debit out of users instead of credit.

In those cases, I'll say "no" and make them pay the fees.  Ultimately, though, it's probably like those annoying pop-ups on websites to sign up for their newsletter -- irritating, but effective.
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