As a full-time Maryland resident, that had to travel for work, can I claim a credit for the Philadelphia local tax taken?

Yes, its possible to claim a credit for these taxes on your Maryland return.

• When working through the Maryland program, go through the Income screens and you will get to the Deductions and Credits section
• Scroll down to Other Credits and click Credit for Taxes Paid to Another State 
• Say Yes to Credit for Taxes Paid to Another State (even though it says not to for PA at the bottom - this is because of the reciprocity agreement)
• Select PA from the list on the next page
• Enter the amount of income that was double taxed and the amount of taxes paid (only enter your local income tax paid)
• You will get a warning about the Reciprocal States to make sure you understand that you should not be claiming a credit for the wages subject to the reciprocal agreement - you can answer No to this because these local taxes are not covered by the agreements
• You should get looped back to your tax credit summary showing the tax credit you are receiving for taxes paid

From Maryland Form 502LC Instructions:

SPECIAL NOTE: If you had wages subject to tax in a locality of Pennsylvania, you may file Form 502LC to claim a State and local tax credit. Enter the amount of tax that you paid to the locality on line 11 of the Form 502LC.

http://forms.marylandtaxes.gov/current_forms/502LC.pdf

Just chatted with Maryland Comptroller office. Seems that a claim e-filed like this will likely be denied at first, because PA return would show $0 in state tax and 502CR apparently does not go in with efile. An amendment would need to be filed, if denied, using the explanation box to outline the Philly issue, along with the 502CR.

@Chico D. Mann Thank you for the update and clarification for others.  I had been thinking of recommending that you paper file the return and include a copy of the nonresident local return showing the tax paid.  Problem is Philadelphia doesn't require you to file such a return when the tax was properly withheld by your employer, so you wouldn't have one.  In my PA locality, we still have to file a local return so you would have one here.  I am surprised that they would want you to file an amendment though and not just respond to a notice with explanation/proof of the tax paid.

@TurboTaxAnthony - Thanks again for the insight. FYI - my e-filed return was accepted by Maryland, and I have received my refund. I will now send in a 502X to amend my return from last year, since I did not claim the locality tax deduction.