Tex. Civil Practice and Remedies Code § 172.060

(a) If a challenge under Sections 172.059(b) and (c) is unsuccessful, the challenging party, not later than the 30th day after the date the party receives notice of the decision rejecting the challenge, may request the district court or the division of the business court of the county in which the place of arbitration is located to decide the challenge.

(b) The court shall sustain the challenge if the facts support a finding that grounds under Section 172.057 fairly exist.

(c) The decision of the court is final and not subject to appeal.

(d) While a request under Subsection (a) is pending, the arbitration tribunal, including the challenged arbitrator, may continue the arbitration and make an award.