You'll need to file a non-resident Maryland tax return in addition to your home state Delaware return.
DE can tax all your income. MD can tax the income you earned from work physically performed in MD.
You'll be able to take a credit on your DE return for the taxes paid to MD, so you won't be double-taxed.
In TurboTax, it's important to complete your non-resident state return BEFORE you do your home state return, so that you won't be double-taxed. See this FAQ for instructions: https://ttlc.intuit.com/questions/1901271-how-do-i-file-a-nonresident-state-return
Location of the employer's home office is irrelevant. Your state tax obligations are based on where you actually live and work.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
