They argue that the marriage equality law does not give LGBT rights to money from taxpayers.
The Texas Supreme Court has ruled unanimously on Friday that same-sex couples working for the City of Houston may not be privy to the same rights as their heterosexual counterparts.
They court overturned a previous decision made by the lower court which favored benefits and sent it back to a lower court.
Anti-LGBT conservatives are hoping that this issue will slowly undo benefits or rights to them made possible by the 2015 SCOTUS decision on marriage equality.
"Marriage is marriage and equal is equal. We will take steps to protect these families," said Kenneth Upton Jr., Dallas-based attorney for Lambda Legal.
The Republican-dominated Texas high court had previously refused to hear the benefits case after SCOTUS ruled that is was unconstitutional to disallow same-sex couples to legally marry.
But, under pressure from Gov. Greg Abbott, Lt. Gov. Dan Patrick and Attorney General Ken Paxton and other religious and conservative groups, the Texas high court agreed to hear the case again.
A state district judge quickly issued an injunction which prevented Mayor Parker's order; the City then responded with an appeal.
However, as marriage equality became legal in 2015, an appeals court lifted the injunction.
Then in March, the Texas Supreme Court heard both sides of the argument once again. The opposition saying that the SCOTUS ruling did not make it a right to provide benefits to LGBT married city workers.
The City countered saying the marriage equality ruling indeed meant that same-sex marriages were to be treated equally.
On Friday, The Texas Supreme Court agreed that SCOTUS’s ruling did not make rights inherent to same-sex couples, sending the argument to the lower court to be straightened out.