Learn Finnish: En tiedä reklamaatiosta mitään, koska hän lähetti sen kirjeitse. - I do not know anything about the complaint, because he sent it by letter.

The ending -tse is the prolative case, used for routes or means of communication. A strict rule for the prolative is that it attaches to the plural stem of a word, even if the meaning is singular in context. The plural stem of kirje is kirjei-, so we get kirjeitse. Here, it just means "by letter," not necessarily that multiple letters were sent.

Could I just use the adessive case and say hän lähetti sen kirjeellä?

Yes, kirjeellä also means "by letter" and is perfectly grammatical. However, the prolative form kirjeitse is an established, slightly more formal way to express means of communication. It fits very naturally with the business context of sending a complaint (reklamaatio).

Why is the word for complaint in the elative case (reklamaatiosta)?

This is a verb rection. When you are talking about knowing about something, the verb tietää (to know) requires the elative case (-sta/-stä). Therefore, "I know about the complaint" translates to tiedän reklamaatiosta.

Why use the form sen for "it" instead of the partitive sitä?