My teenage daughter lives in DE and earns income only in MD. Why does she have to pay $69 to DE?

[TomD8]

A resident of DE is subject to DE income tax on all their income, regardless of where earned.

MD can tax non-residents on income earned from working in MD.

Thus your daughter has to file in both states.

She'll be able to claim a credit on her DE return for the taxes paid to MD, so she won't be double-taxed.  But the credit may not cover her entire DE tax bill.

[LenaH]

As a resident of Delaware, she is responsible for tax on all of her income (no matter where it is earned) in her resident state. 

If she earns income in Maryland, she will also file a nonresident return for the state and be responsible for tax on income earned in Maryland. However, Delaware will give her a credit of taxes paid to other states to prevent double taxation. 

Please ensure she is taking the credit of taxes paid to other states. As she is going through the return, she should come to a screen titled Credit for Taxes Paid to Other States. Answer yes to the question Did you pay income tax to another state? and follow the on-screen instructions.