We sentenced someone to State Jail and then let Tarrant County come get her for their hold. Somehow the TDC hold did not get placed and Tarrant County let her out. What procedure/capias do you use to get her into TDC custody?

It would appear to me that you should request the convicting court to issue a capias. See Holloway, 329 S.W.3d at 255. See also art. 43.015(1).

You want to try to avoid, as much as possible, application of Ex parte Baker, 297 S.W.3d 256, 259 (Tex.Crim.App.2009) (habeas applicant entitled to credit for time when he was erroneously released after completing a sentence in Harris County when he should have remained in confinement to complete another sentence imposed by Gillespie County).