The State of Texas has changed the rules of the eviction game. The process related to the CDC eviction moratorium in Texas eviction cases has been governed by the Texas Supreme Court’s Emergency Orders, not the specific text of the CDC order itself.
Nothing in the text of the moratorium itself specifically directs or forbids courts to take any action.

Instead, it directs landlords to not evict tenants that are covered by the moratorium. It also provides civil and criminal penalties for landlords who violate the moratorium, but that is a matter between the tenant, the landlord, and potentially a federal prosecutor.
It is not a matter that a justice court can or should enforce in the absence of authority from the Texas Supreme Court.

The issue to consider is whether the risk of a federal lawsuit is legitimate enough to hold back from an eviction before the Moratorium ends.