So I've seen quite a few people saying how you could learn the more basic parts of the language through exposure to it. I just want to say a few things about how that would be a lot easier said than done.
(I am no linguist by the way, but I do know a decent amount of another language (Irish) that I will refer to here for examples of how things could get complicated. And yes, I do agree that it is a bit sad that the MC has made seemingly little effort to learn the language.)
First of all, I would agree that you could learn some of the more basic things like "Hello", "yes", "no", or even "Thank you", but it would still take a long time, and in some cases, might not be possible. As an example, in Irish the way you say hello and thank you changes slightly depending on whether your talking to one person or multiple people. As for "yes" and "no", Irish doesnt actually have words for "yes" or "no". For all we know, this language may also lack words for things we take for granted, and that would complicate things quite a bit.
Second, about nouns. Simply put, you could potentially learn the basic form of a noun by pointing at the object you want to learn and hoping they respond with whatever it is, but that isn't much use when the noun is pronounced quite differently depending on the context and the grammar of the language.
As I mentioned above, there is also the possibility of words not existing in her language that do in his, and that idea is expressed in a very different way in her language. This applies to both nouns and verbs. (Just as an example for verbs, Irish has no verb for to have, nor verbs for to like, love, dislike or hate). This also works the other way around aswell, when some form of a word or single word exists in her language that may not exist in his, which would complicate things further.
I would like to say again, I agree that its a shame the MC hasn't even tried to learn a small bit, which is alot of missed potential for various misunderstandings and the like, but I just wanted to let some people know that learning a language, particularly one that is drastically different or has complex grammar rules, is fairly difficult, especially without anyone who speaks your own language or a language you speak to teach you.
Okay, rant over. If you read all this, sorry for wasting your time with my ramblings.