question- Is there a restriction on issuing VISA check cards to non US citizens? For those who offer this product, how do you handle applications received from non US citizens??
Thank you for you input.

There are a couple of questions that you need to consider.
1. Are they a resident?
2. If they are a non-resident, does your bank have policies against lending to non-residents?

In many banks, residents are treated the same way as citizens. I would think you could have fair lending issues with your regulator if you do not lend to legal residents. As far as lending to non-residents, there are strong arguments for not lending, such as collection, etc. If you choose not to lend to a non-resident (i.e. you decline them for that reason), you're bank's lending policy needs to address that.

Check your VISA issuance regulations. For normal VISA card issuance, VISA use to prohibit the issuance of cards to non-US citizens.

A VISA check card would not be "lending" - it is basically a debit card. It would seem to have the same requirements as opening a bank account.

One concern might be that it could be used to transfer funds across national borders.

Again, I would urge you to check your card issuers rules. VISA USA use to prohibit the issuance of cards to non-U.S. citizen.

This is VISA territory all the way. If they an open an account at your bank, they can have the card. Unless you are talking about one of these new prepaid debit card programs...that is a different story.