Grandpa Alexander H.D. "Hammy" Hurt probably didn't have a Texas Ranger badge issued to him. According to a Ranger history piece posted on the Texas Ranger Hall of Fame and Museum:
"When the Frontier Battalion and Special Force were formed in 1874, it was difficult for Texas Rangers to establish their authority. The State of Texas Adjutant General's Office began issuing Warrants of Authority -- impressive paper documents kept folded in their pockets -- to officers but not to enlisted men. This practice continued, in one form or another, until 1935 when badges and credentials were specified for all Texas Rangers."
But we do have his service record and pension papers that document his service in the Texas Ranger Frontier Battalion, Company F.