Why you need a check or credit card to save your tax?
For salary income, those check/credit card amount will be a tax deductible expenses with 3mil.won maximum. Once you wiped 13mil.won while earning 30mil.won salary income, you can deduct around 3mil.won and can save 200,000won-450,000won income tax at the year-end settlement.
So you need a check(30%) or credit card(25%) to save tax, and most likely check card since a lot of bank reluctantly issue a credit card if you hold the E-2 VISA.
When you issue a check card, you can also ask to embed a transportation card(교통카드) function with VISA or MASTER for wiping abroad if you wanted.
You can register the credit/check card at the NTS Hometax website, it's automatically record your spending and issue a certificate during your year-end settlement period in January.
Otherwise you can visit a bank deal with and ask them to issue "신용카드등 사용확인서-소득공제용" in person to submit it to your employer.
More details, please send me an email to firstname.lastname@example.org