Translation:What was in the letters that were on the table?
One native AmE speaker's thought...
"What WERE in the letters" sounds REALLY strange. Presumably, we're asking what the letters were about. So if we said, "What WERE the letters about?" that would be fine (but that's not the Czech sentence). And if we said, "What WAS in the letters," that also would be fine. But I can't think of a situation where "What were in the letters" would make sense...
This is a kind of topic where I really can only follow the advice of other people or grammar rules from books.
I tried to search for this usage and found these. It seems to be very rare though: https://www.google.com/search?q=%22what+were+in+the%22&lr=lang_en&tbs=lr:lang_1en&tbm=bks&ei=3OFZW7rfKIXp6ATZmLDABg&start=10&sa=N&biw=1112&bih=480&dpr=1
We probably cant expect there were some individual items in the letters, but some uncountable content so perhaps it is wrong to even allow were here?
I was thinking about this again this morning. So my updated "thought" is...
To me, the question is about the content of a letter, not the content of an envelope in which the letter may be.
So the implied question is really "What (information) was in the letters," and "information" would require "was."
Now, we could also suggest that the question is really "What were (the contents of) the letters," and "contents" would use "were."
BUT... neither "information" nor "contents" is actually in the sentence. So without either of those words to guide the choice of the verb, "was" sounds perfectly normal and "were" sounds extremely weird.
OK, I found the relevant rule:
In general, the interrogative pronouns who and what take the default value of singular. … The default singular values for who and what can, however, be overridden when there is a presupposition that the answer is plural: …
We have multiple letters, so presupposition is possible, I guess, so I will add it.