An amendment of this type, due to your unique situation, should be mailed in - and send Certified Mail/Return Receipt Requested. That way when they receive it and sign for it you will then receive back the "green card" that they signed and this is your "Return Receipt".
If what I am reading is correct and that you still owe Delaware (i.e. - you have not yet paid them) do not pay them.
So, if your home of record (domicile) was Texas when you joined the military, you remain a resident of that state, even if you are stationed in the other State. This other State is your "non-resident" State for tax purposes.
Here is a link with some helpful information for your situation:
Military State of Residence For Income Tax Purposes
