William
Was it objectively speaking the better idea to stay with this person, go get something to eat in a warm place, and only then leave? Sure. Food was something the Doctor desperately needed on the best of days, and warmth would be great right now, considering how cold it was in this damned country. However, their appetite was nonexistent currently, and their desire to spend more time around people when they were already exhausted, even less so. All they truly wanted was to curl up somewhere and sleep, no matter how much the stranger might desire company.

Frankly, the only thing really keeping them here was the fact that her injuries hadn't entirely been fixed, but she seemed stubborn enough to not let them do that. Why waste the energy? They did what they could, no? Having stitched it up, it should start healing, assuming the wound was taking care of - and considering the scars she mentioned, the woman was likely used to getting injured like that, so she probably knew how to do so.

All in all, it seemed that there was no real reason for them to stay. The Doctor straightened their back somewhat, making an attempt to look her in the eyes. "Make sure to keep your wound clean," They told her, stuffing their hands into their pockets. "And..." They wouldn't normally add a statement like this, but it felt important right now, "I hope you stay safe." Was that all? Seemed like it was about time for the two of them to part ways - unless she had something else to add, of course.
Lelah
*Oryra could tell at her saying they could leave that it probably would happen just like that. She didn't blame them, she'd kept them out in the cold long enough. Hopefully they would get somewhere warm once they did leave.

Holding back wanting to say more was hard yet she did. She'd been stubborn enough for this doctor. She might seem them again someday though she really doubted she would. If the law didn't get her who knew what would be next.* "I will keep it clean. You don't need to worry about that... I will try my best, not much I can do though."

*Taking a deep breath she would close her eyes. The cold was almost nice to her because it kept her from saying something to make them stay. Oryra opened her eyes as she looked at the doctor a last time.* "Get back safe, no need for you to get sick being out longer." *With that she turned from the town and walked a side ways from it, to where she didn't know.*
William
There were plenty of things one could do to stay safe, but the Doctor didn't mention it, not wanting to risk annoying her at the end of what had otherwise been a relatively pleasant meeting. Instead, they just gave a nod, raising a hand in a half-hearted wave as they watched her leave.

And just like that, it seemed like it was time for them to go as well. The Doctor exhaled a sigh, then turned around, stuffing their hands deep into their pockets. They had meant to wander around the city a little, see what it had to offer, but, well... Seemed today wasn't the day - though as they started walking, they soon realized they weren't unsatisfied, it was quite the opposite.

What better way was there to spend their time and energy than to save someone's life? Make sure someone got another day to live? Despite their exhaustion, when they started walking back, the Doctor was in a good mood, head held high and looking ahead instead of down at the ground. They'd done good, and they were allowing themself to be a little proud of it.