Again, I have no idea what this sentence means. The son of the turnkey at the debtor's prison is in love with Little Dorrit, who has begged him not to mention it again. So he is depressed, and his parents are hoping to get help from Mr. Clennam.
"
'It's the only change he takes,' said Mrs Chivery, shaking her head
afresh. 'He won't go out, even in the back-yard, when there's no
linen; but when there's linen to keep the neighbours' eyes off,
he'll sit there, hours. Hours he will. Says he feels as if it was
groves!' Mrs Chivery shook her head again, put her apron in a
motherly way to her eyes, and reconducted her visitor into the
regions of the business."

perhaps he's longing for the woods?

Well, the only thing he can see is the posts of neighbors clotheslines.

I think the idea is that for John the back yard is as refreshing and beautiful as if it were a woodland scene.

Bingley

that's what I was thinkin'