change filing status on 2019 return (amendment)

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

No, we paid the money last year when we completed our 2019 return. So, we need to get that amount refunded. My husband's state of residence is Texas and I indicated that on turbotax when I completed my file. I was a resident of DE before we got married. So, I'm trying to file an amendment to change the filing status but the turbotax amendment program isn't letting me.

TurboTax will not allow you to change Delaware to married filing separate if the federal is married filing joint. So first create a mock married filing separate federal return in order to get Delaware to give you the option to create a separate return.

 

You can amend your return using TurboTax CD/Desktop. After downloading and installing the amend software, create the mock married filing separate federal return.

• Delete all your husband’s income and any specific deductions. If you itemized deductions, you will have to decide how to divide them
• Change the filing status on federal from joint to separate in Personal Info
• Then go to State and keep going until you reach Change a Previous Delaware Return. Say Yes and amend

This link has some helpful information: How do I prepare a joint federal return and separate state returns?

If your active duty servicemember spouse's State of Legal Residence is TX, the VBTA Act of 2018 permits you to declare TX as your State of Residence for tax purposes, even if you've never lived there - thus making your 2019 income not taxable by Delaware.  Here is the text of the law, with the relevant wording highlighted:

 

SEC. 302. RESIDENCE OF SPOUSES OF SERVICEMEMBERS FOR TAX PURPOSES.
(a) Residence for Tax Purposes.--Section 511(a)(2) of the
Servicemembers Civil Relief Act (50 U.S.C. 4001(a)(2)) is amended--
(1) by striking ``A spouse'' and inserting the following:
``(A) In general.--A spouse''; and
(2) by adding at the end the following new subparagraph:
``(B) Election.--For any taxable year of the
marriage, the spouse of a servicemember may elect to use
the same residence for purposes of taxation as the
servicemember regardless of the date on which the
marriage of the spouse and the servicemember
occurred.''.
(b) <<NOTE: 50 USC 4001 note.>> Applicability.--The amendments made
by subsection (a) shall apply with respect to any return of State or
local income tax filed for any taxable year beginning with the taxable
year that includes the date of the enactment of this Act.

https://www.congress.gov/bill/115th-congress/senate-bill/2248/text

The tax consultant from Military OneSource told me that as well; however, the DE tax auditor told me that because I filed as resident in DE for several years prior to the marriage, I was not eligible for that, as I did not move to DE to be with my spouse. I was already residing there.

In my opinion the Delaware tax auditor is incorrect.  The VBTA doesn't contain any such requirement.  In fact it states that the date of the marriage doesn't matter.  The web reference in my original answer gives you the exact text of the law.  Unfortunately my opinion is unofficial, and won't carry any weight with DE tax authorities.