Translation:This is the letter which I wrote.
This is one of several English translations that uses "which" when it should be using "that." I know the latter is also accepted but the repeated glitch grates on my ear a little. From an English grammar: "If the sentence doesn’t need the clause that the word in question is connecting, use which. If it does, use that."
From another English grammar source ( https://www.dictionary.com/browse/which?s=t ):
Contrary to the teachings of some usage guides, which introduces both restrictive and nonrestrictive clauses. The “rule” that which can be used only with nonrestrictive clauses has no basis in fact. In edited prose three-fourths of the clauses in which which is the relative pronoun are restrictive: A novel which he later wrote quickly became a bestseller.
English doesn't have an Academy of the English language which publishes the One Single Authoritative Grammar Book; there are multiple competing grammar and style guides which sometimes contradict each other, as in this case.
In my opinion, your source is talking through his or her hat, excusing the bad style of writers such as the one who is quoted. When in doubt on any point of English grammar or style, I consult Strunk and White, The Elements of Style (4th Ed.) They say: " 'That' is the defining, or restrictive, pronoun, 'which' the nondefining, or nonrestrictive. . . .The use of 'which' for 'that' is common in written and spoken language. . . . But it would be a convenience to all if these two pronouns were used with precision." (Id. p. 59.)
While there is no Single Authoritative Grammar Book for the English language, The Elements of Style is as close to one as you can get, at least for American English.
Languages are living things which (that?) evolve naturally as time passes. People are always coming up with new words / expressions / punctuation etc. This applies to the so called "rules of grammar" which are really just an attemp to formalise the way people construct sentences in any one languague. In reality these rules change based on location and with the passing of time. A good case in point is the use of "whom" as a relative pronoun in the accusitive. This has now fallen out of fashion and is used far less amongst the general population, being replaced with "who" instead. In 100 years I imagine the "rules" won't mention "whom".
A book written 100 years ago doesn't reflect how a language has evolved. You'll find in practice that most people (at least in the UK) use "that" and "which" interchageably when it comes to it's use as a relative pronoun, at least in my experience.