Local tax paid to reciprocal state

You will not be able to get a refund of the tax paid to the City of Philadelphia.  According to the city:

The Wage Tax is a tax on salaries, wages, commissions, and other compensation. The tax applies to payments that a person receives from an employer in return for work or services. All employed Philadelphia residents owe the Wage Tax, regardless of where they work. Non-residents who work in Philadelphia must also pay the Wage Tax.

All employers located in Pennsylvania are required to register with the City of Philadelphia within 30 days of becoming an employer of either:

• A resident of Philadelphia, or
• A non-resident of Philadelphia who performs services for an employer in Philadelphia.

Employers are required to withhold the Wage Tax from all employees who meet these criteria.