Albert Barnes Commentary 1 Samuel 24:22

"And David sware unto Saul. And Saul went home; but David and his men gat them up unto the stronghold." — 1 Samuel 24:22 (ASV)

Saul does not appear to have invited David to return to Gibeah or to have given him any assurance that he could do so safely. David, with his intuitive sagacity, perceived that the softening of Saul’s feelings was only momentary and that the situation remained unchanged.