There is an advantage to the debit card. It takes from your checking account and will not let you overdraw. Since you are not overdrawing on your accounts, it does help your credit report. Not being late or past due on debts will help quite a bit in making your credit score better. It may not put it on the roof but many people going through a divorce are just scraping by and to give them a credit card which can easily draw them to buying more than they can afford is not going to help their credit score either.
this is incorrect Wolfy. if you draw out more than is available in your checking account it will 'let you overdraw" and you will be charged bounced check fees. Your debit card is basically an electronic check.
Your credit score is an "i love debt score" the more you charge and pay back on time the higher it goes. If you don't ever charge anything, you don't have a credit score.