To be honest, the employer didn't make the mistake. Furthermore, the employer can't just fix it by issuing a corrected W-2 - because they have already sent that withheld money to the state of Delaware who won't want to give it back.
To get that money back, you will have to file a Delaware return.
I am not sure that you even owe any Delaware tax, since you were never a "resident" in the tax sense. You were likely a resident of New Jersey the entire year (even when you were temporarily relocated to HK). And you don't have any Delaware source income that I can see.
And if you even owe any Delaware state tax, it is likely that New Jersey will credit you for taxes paid to Delaware - most states actually do try to avoid double-taxing your income.
This is just the result of a simple misunderstanding that you did not realize that when you changed your mail address, the payroll department took that to mean that you moved to Delaware in order to work (in which case you would have been a resident or had Delaware source income or both).
You will just have to bite the bullet this year and file two state returns.
