Aside from what his sister says about him, how does the reader know Framton is uncomfortable meeting strangers?

Framton Nuttel is a highly-strung young man who's been sent on a rest cure to the country by his doctor, to help soothe his frayed nerves. His sister thinks it would be a good idea for him to get out and meet new people during his stay. So she gives him letters of introduction to some local families, one of which is the Sappletons. While visiting the Sappleton residence, Framton starts chatting with the mischievous Vera. As their conversation begins, Framton's awkwardness with strangers is much in evidence:

"Do you know many of the people round here?" asked the niece, when she judged that they had had sufficient silent communion.
"Hardly a soul," said Framton. "My sister was staying here, at the rectory, you know, some four years ago, and she gave me letters of introduction to some of the people here."
He made the last statement in a tone of distinct regret. (Emphasis added).

In other words, Framton's none too pleased that he's expected to go out and meet new people during his rest cure in the country.
It's notable that, during this conversation, it's Vera who does much of the talking, indicating once more that Framton's deeply uncomfortable in the presence of strangers. And later on, when Mrs. Sappleton appears, it's telling that she barely manages to stifle a yawn as Framton manfully tries to make small talk about his various ailments. He clearly is no conversationalist, and is visibly ill at ease with people he doesn't really know.