According to the Texas Department of State Health Services, a person has to be at least 18 years old to get a tattoo in Texas. Under supervision of a parent, a minor is allowed to have a tattoo covered or removed.
Wikipedia mentions that a parent is allowed to have a minor's tattoo covered if it contains offensive language, gang symbols or other markings that the parent deems necessary for removal. The National Conference of State Legislatures notes that the physical presence of a parent, or proof of parentage, is required. Khou.com notes that Texas law requires tattoo shops to record the type of identification a customer shows to verify age. Only the type of ID shown is required and not the number or photocopy.