He had no claim over the priestess, but that didn't mean other males were free to do so.

Sesshoumaru tolerated Kagome simply because she took excellent care of his ward in ways he was not capable of. She showed bravery and did not back down from the evil Spider even at the brink of death. Loyalty to her pack was something else he admired about her, even when those companions eventually abandoned her one by one. The day he tracked down her whereabouts with a younger Rin in tow he had discovered the two years she spent alone had taken its toll. Kagome was much too thin and skittish and had become a shadow of the bright young woman she had been when he had witness her complete her quest.
From that day on Sesshoumaru had insured she remained healthy and content so that his ward would be given the knowledge only the priestess could provide. As the years went on, he had seen her slowly coming back, she was no longer the young brash girl he encountered in his father's tomb, now she stood a strong woman who has learned how to survive in a world foreign to her.
Yes, Sesshoumaru credited himself on 'fixing' the priestess. He would not let all his work be tarnished by a pup who did not know how to act around a human female.

"Rin, go help the priestess with her tea ritual." Not bothered by her lord's dismissal, Rin leap up to do as she was told in hopes of filling his ears once more with ways to treat a rash made by the poisonous plant.
In a blink Sesshoumaru stood before his lieutenant with a hard look in his eyes. Immediately the young soldier dropped to kneel before his lord. Pleased at this sign of submission he rumbled, "You would do well not to place meaning where there is none, pup." Masaru gave a sharp nod and tilted his head to the side to expose his neck. "If This Ones returns to find the priestess or ward no longer in the pristine condition he left them in," he paused as crimson began to tint the corners of his eyes and his bestial side bled into his voice, "we will bleed you dry then feast upon your flesh so only bones remain for your family to mourn."
The spike in Sesshoumaru's aura caused Masaru to sink lower to the ground until his face hovered just above worn leather boots.
Just as quickly as the burn of his lord's power hit him it was gone. He remained still not daring to move an inch until told otherwise. Masaru was a fast learner and had no intentions of repeating his shameful behavior, by disrespecting the priestess Lord Sesshoumaru was well within his rights to do more than verbally reprimand him. It was not his place to question the nature of the demon lord's relationship with the human woman and he had no intention to. She bared no mark or claim but that meant nothing while already under the demon's protection.

"Rise lieutenant, it is time you meet those whose lives now rest in your hands." The loosely veiled threat was heard loud and clear, they die you die.
Back on his feet Masaru followed the powerful demon lord back to hut. Both males removed their boots before entering and stood before the humans.

Kagome had just finished arranging the last place settling when the demons stepped in, her home felt entirely too small with them in it. Once Rin set down the last of the side dishes to go with the light lunch and tea, she took her place in front of Kagome and waited for her lord to speak while the priestess placed her hands on her shoulders.

The sight they made had Sesshoumaru wanting to take in every detail and immortalize this image in his mind. Rin's orange kimono and green obi brought back an air of nostalgia and visions of a child with missing teeth and side ponytail smiling up at him. He missed how easy it was to please her then, a field of wildflowers was enough to keep her happy and content for days. Now his ward was on the precipice of womanhood and no longer held the same childlike innocence she once did. Would she be wed to some human male upon his return? Or mated to a demon and raising her own offspring? The thought made his blood run cold.
Sesshoumaru was pulled from his inner turmoil by the movement of the priestess's hand. He watched as she reached up to smooth back Rin's wild chestnut hair and gather it into a low elegant bun.

Somehow the priestess's physical changes were more obvious to Sesshoumaru. The deep lavender robe she currently wore was a welcome change from the revealing clothes she once sported that showed off her scrawny limbs.
Though she was still quite small by human standards, her head only coming up to his wide chest, her appearance had undoubtably matured. Thin legs had turned into lean muscles to support her widened hips. Her small waist was easy to see now that she mostly wore simple robes that cinched when tied. Loose sleeves hid her toned arms but stopped at the wrist to show small hands, the feminine tops of them gave no hint to the callus palms and fingers just below showing years of bow training and physical labor. While her chest remained covered it was difficult to ignore at times since Kagome opted to continue wearing the bindings from her homeland and not the typical cloth wraps village women drone. The strange garments showed off the fullness of their size and seemed to squeeze them together to create a pleasing sight. Waves of ink blank hair framed her heart shaped face, large ocean blue eyes, and full lips.

The sound of the priestess clearing her throat brought Sesshoumaru back from his thoughts.

"This Sesshoumaru presents Lieutenant Masaru Sakai, son to the Western Lands military advisor General Katsu Sakai." The blonde demon bowed to the priestess and ward.
"Until released from his duties, he will be responsible for the protection and wellbeing of Lady Kagome Higurashi the Shikon Priestess," the demon lord made a vague gesture in her direction while the lieutenant bristled at her title, "and Lady Rin, Ward to Western Lands."

A loud clap brought the room's attention to Kagome. "Well, now that's done shall we eat?"