You must submit a non-resident tax return in MD in addition to your home state tax return in DE. You'll be able to take a credit on your DE return for taxes paid to MD. In TurboTax, complete your non-resident state return before your home state return in order for the credits to flow correctly.
You'll find the allowable subtractions from your MD income on page 4 of this reference: http://forms.marylandtaxes.com/11_forms/nonResident.pdf