Hi there, unfortunately Delaware and Maryland do not have a reciprocal agreement for tax payment.
This means that you will need to file a non-resident return for Maryland (you can file jointly) and report your earnings on your Delaware resident return.
Your employer should have withheld Maryland state tax (not county tax).
You will need to pay tax to MD on your earnings, and you will be allowed a credit for taxes imposed by another jurisdiction on your Delaware return.
See the DE website which will explain this situation, scroll down to DELAWARE RESIDENT WORKING OUT OF STATE
You will need to file a Maryland non-resident return to report your MD income. You most likely will have a balance due to pay to MD. If you are still working for this company, you should advise your employer to begin withholding MD state tax immediately.