Link is used to running -- more used to it than he probably should be. The pound of his heart, his paws gliding over the ground. Most of the time, hes running towards something -- a monster, maybe. One of those warped creatures that inhabited the land, the groups, around Hyrule. He hasn't seen any here, not for miles.
He doesn't know when he got here, so far past the other groups. So far away from what was apparently supposed to be his duty. He didn't ask for this. He didn't ask to wake up without his memories, to be tasked with saving so many people. Link didn't even know what it meant to be a hero -- all he knew was that he was one, and it's weight is like lead on his shoulders.
Helping people made him feel good. He liked it when Sidon thanked him so profusely for taking down the giant beast of their group, the relieved sighs of the people as he tore down the foe terrorizing them. But that was all. People expected him to save them. The work was thankless.
He didn't ask for this.
Which is why he doesn't immediately double down once he realizes how far he's come from where he was supposed to be. Miles and miles -- it was hard to tell where you were, deep in the wilderness. Granted, crossing over oceans wasn't really capable of being an accident, which begged the question of how he got here to begin with. Ears lie back warily.
He knows forests. Forests are familiar -- though nowhere near as safe as mountains. He remembers the monsters crawling all through the woods.
There's no scent of them now.
He can recognize signs of civilization, however. The scent of the air, pawprints in the dirt. Link's expression is guarded. Civilization is safe, he knows this much. He does not know what it is like outside of Hyrule -- Link's lack of memory proves this, but he can't help the lack of wariness. Not to say he's not wary, he is. Just not enough. He takes another few pawsteps, ears straining to hear. Where were they? He wonders if they'd mind if he stayed a while. He's so tired, too tired to go back and to continue his great quest. .. Not like he knew what his quest was all about, anyways, besides to protect people, to tame the divine beasts.
So, maybe, it just doesn't matter.
//sorry this is kind of disjointed
(lore info cause this is kind of confusing: basically its just loz as animals. monsters, divine beasts, ganon, etc, are all just,,, big op animals. he never really learned what his quest was all about.)

Link heard the approach, of course. He'd tensed, even so, starting just so slightly when the tabby comes into view. His slight puzzlement is obvious in his body language, though it doesn't occur to him to find the other's crashland funny. He tilts his head, barely hears what they're saying. Except that he does. It's somewhat startling, how quick the offer is.
Link does not attempt to answer, yet. Instead, he approaches the fallen feline, and attempts to, wordlessly and somewhat thoughtlessly, pick them up by their scruff and lift them up enough to steady them. If he manages it, he will step back a few more steps, though not quite enough for comfort. He hasn't quite grasped 'personal space' yet -- he hasn't interacted with people enough to notice.
He considers the option again. .. It almost feels like a betrayal to whatever his unknown duty may be to abandon it, even temporarily, in favor of this. But Link doesn't know how to go back, so he ... he supposes it doesn't really matter. A long moment of pause, and Link dips his head in a nod. He makes no move to introduce himself, merely nods in acceptance. It genuinely doesn't occur to him that people might want his name -- people had never cared. Some had already known it(they knew it before Link did, really.), or they just hadn't cared to know. Which, incidentally, is a path that wouldn't be followed here. His reach had only ever extended to the edges of Hyrule, after all, and even then, dubiously. A hundred years is a long time, though, especially for animals.

Link remembers hearing a lot about him giving up his life for Hyrule. He doesn't remember it, of course -- but he knows it happened. Link still isn't quite sure how to feel about it. Maybe he doesn't. His feelings about his past, where there weren't any memories, were clinical at best, for however much he regretted the gap of them.
Link regards Jerseyboy with a strange sort of flatness, though his head is still tilted. A lot of things about people or civilization don't occur to him -- the fact that the small tuxedo is being rude is one of these things. He wouldn't even be bothered, except for the other's mention of talking. Link understood that talking was important to people -- the people where he came from weren't usually bothered, but he could tell that they sometimes got frustrated by his unwillingness to talk. Link shakes his head to Jerseyboy's 'question', but contradicts himself moments later. ".. Link," He says, voice hoarse from disuse. Trying to talk is like .. he's not sure. It's hard. He doesn't like it, and it always makes him feel .. unsafe, uncomfortable. So, if he can help it, he doesn't. Charades are fine, though difficult -- it's just a shame that animals couldn't use sign language effectively, honestly.