How do I respond to a certified letter from Berkheimer stating I owe them $700 for an earned income tax discrepancy in 2019?

What is Berkheimer?

That is the company that administers most of Pennsylvania's local/city taxes.

https://www.hab-inc.com/

Yes respond ... either they are correct and you need to pay up  or they are wrong and you send them proof of their error. 

When you receive a letter like that from a legitimate taxing authority, you have two choices: either pay the amount they say you owe or protest their finding.  Normally letters of this type contain instructions on how to appeal or protest a finding with which you disagree.