Given the context, how about: when the writer wants/tries to say [Japanese expression] in English, it's a problem for them (b/c they don't know how, it's awkward or sensitive, etc.)?
(I'm assuming the content of [something] can't be interpreted as a description/type of とき.)
とき is presumably 時 (used here a bit like conjunctive と)
困る is one of those very common, useful, vague words. It has a few different senses depending on context: troubled, embarrassed, don't know, inconvenienced, annoyed, at a loss, etc. It can be used as an indirect way to tell someone else not to do something ("If that were to happen, I'd be inconvenienced..." lol) or simply a description of the (mildly to strongly) negative predicament or reaction to some event or circumstance (I lost my passport and didn't know what to do.) If you read through some dictionary example sentences, you should have a good feel for its use.