On his way to the Citadel of Oldtown, Samwell Tarly stops at his family's fortress. Sam's relationship with his father is not good and on top of that Sam had brought a wildling girl with him.
Sam's father, Randyll Tarly, hates Sam, since he could not make a "good heir" from him.
When Sam turned fifteen, his father bluntly told him that he was not worthy of their house's ancestral Valyrian steel sword, Heartsbane, and that he must join the Night's Watch and renounce his family name so that he would not stand in the way of Dickon's inheritance.
During this visit Sam's father keeps teasing him that he is going to the Citadel "to read about the great quests of other men".
Nevertheless, when Sam leaves his family's manor, he takes with him their house's ancestral Valyrian steel sword.
It should be clear that Sam, Gilly, "their" baby and a such a precious artifact as an ancestral Valyrian steel sword disappear at the same time (or almost).
Why didn't Randyll Tarly ever investigate the disappearance of the sword and/or track Sam in order to recover it?