TBH, I had never heard the term "restricted relative clause" before this, so I did some research (i.e. a lazy Google search).
It appears that "that" and "which" are equally acceptable in British English, but American English has a preference for "that", owing entirely to 19th century grammarians (which puts it in the same category of "rule" as not ending a sentence with a preposition).
Do I infer correctly from the wrong relative pronoun "which" used in the default English translation above that the Swedish language does not distinguish whether relative clauses are restrictive (AKA defining) or not, while such distinction does matter in how a relative clause is constructed in English?
In "The TV that we have is not new", the relative clause "that we have" is restrictive/defining in that it narrows down which TV set we are talking about.
A non-restrictive/non-defining relative clause, on the other hand, merely provides supplementary information, given that it is already clear what we are talking about and there is no need for further narrowing down.
In many other exercises in the relative pronoun section, the English translations can swap out a restrictive relative clause for a non-restrictive clause and vice versa and still remain valid statements under different contexts, but in this case it can work only one way. "The TV, which we have, is not new" would be in the form of a non-restrictive relative clause, but it doesn't make sense as such. In using a non-restrictive clause, we take for granted it is already clear which TV set we are talking about. Suppose we want to add some side information about its ownership, we just wouldn't say "which we have", but rather something like "The TV, which belongs to us (therefore we would know), is not new". Another correct use of a non-restrictive clause would be "This TV model, which we have, is not new."
When referring to a person, the relative pronoun "who/whom" can be used to introduce either kind of relative clause, and the distinction is made only by punctuation and prosody. When referring to an objection, though, "that" is used to introduce a restrictive clause, while "which" is used to introduce a non-restrictive clause. (The relative pronoun "that" can refer to a thing or a person in starting a restrictive clause, and it is never used in a non-restrictive clause.) So, in this translation we mean to use the relative pronoun "that", which might even be left out and merely implied (possible only in the case of restrictive clauses).
Edit: Upon research, I see that the avoidance of using "which" in opening a restrictive relative clause is considered by some not to be a hard rule but a recommendation for clarity. In any case, I would still like to get a confirmation that Swedish makes no structural distinction between restrictive and non-restrictive relative clauses.
I'm noticing that a lot of the sentences in this lesson, this one included, could be formed just as easily in without relative pronouns (both in English and Swedish) and at least in English sound more natural without them ('Our TV is not new.' being the example in this case).
Are these cases of just using the particular construction to teach relative pronouns, or does Swedish just idiomatically use relative pronouns more frequently than English does.
"Which" and "that" are not interchangeable; "that we have" is restrictive, it tells you we are talking about a specific TV. Set off by commas, "which we have" becomes incidental, but without that phrase the meaning is lost (unless you're sitting in the room with the TV and pointing to it as you speak!).
That's true--it's confusing to understand the difference (it certainly took me a while), and it doesn't really matter in the big scheme of things. Still, I felt that a language course shouldn't tell people either usage is the same when there is a difference of meaning. I'm a big admirer of the way Brits write and speak English, but in this case, I lean toward adhering to a practice that enables one to make distinctions and be as precise as possible. Does that make sense?